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Life is strong and & also fragile. It's a paradox. It's both things, like quantum physics:It's a particle and a wave at the same time!

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Life is strong and & also fragile. It's a paradox. It's both things, like quantum physics:It's a particle and a wave at the same time!

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TopNewestThe first and most sensible question:-

Do you like carrots? – Mehul Arora · 1 year, 7 months ago

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– Chinmay Sangawadekar · 1 year, 7 months ago

not really,tell me do you like carrots?Log in to reply

– Chinmay Sangawadekar · 1 year, 6 months ago

Hey Mehul , do you have quadro phobia?Log in to reply

@Otto Bretscher

this and this

Kindly see into those problems...They are getting low response and also they are waiting for your awesome solutions...;) – Chinmay Sangawadekar · 10 months, 1 week ago

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– Otto Bretscher · 10 months, 1 week ago

Looks like everybody is busy at school or work, including myself ;)Log in to reply

@Aareyan Manzoor @Sharky Kesa see this problem......

this – Chinmay Sangawadekar · 10 months, 2 weeks ago

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– Nihar Mahajan · 10 months, 2 weeks ago

404 is a palindrome in base: -31Log in to reply

– Chinmay Sangawadekar · 10 months, 2 weeks ago

Check my profile then...Log in to reply

@Otto Bretscher dsorry to disturb you ...https://brilliant.org/problems/more-problems-in-2016-part-11/?group=JgjXt4dJvxew&ref_id=113 – Chinmay Sangawadekar · 10 months, 2 weeks ago

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@Otto Bretscher

Please look into my latest problem , Gauss won't help,, it is getting a lot of reports , but still I think problem may be right...help me comrade... – Chinmay Sangawadekar · 10 months, 3 weeks ago

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– Otto Bretscher · 10 months, 3 weeks ago

It's great problem and your answer is correct, Comrade. You should write the Legendre symbol more clearly as \(\left(\frac{n(n+1)}{10009}\right)\) thoughLog in to reply

@Otto Bretscher

There is no fun in doing Number Theory without you...:( – Chinmay Sangawadekar · 10 months, 3 weeks ago

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– Otto Bretscher · 10 months, 3 weeks ago

I really don't want to post any more problems... then I have to deal with some of these obnoxious guys when they post solutions. Maybe I will give you some ideas and you can post, Comrade!Log in to reply

– Mehul Arora · 10 months, 3 weeks ago

Oh lord no! Your problems are really integral to the community, sir. Please don't stop posting problems. As Nihar rightly did point out, you may report any such action to the staff, so that appropriate action can be taken. But please don't stop posting problems! :(Log in to reply

– Nihar Mahajan · 10 months, 3 weeks ago

Humble Request: Please don't stop posting problems because of obnoxious guys. You are a crucial part of community and so are your problems. We enjoy your problems very much. If some guys are troubling you by any means , you may report it in private or on message board of any staff and the staff will take the appropriate action. Grooming math enthusiasts and comrades like Chinmay , Aareyan , me need your help on Brilliant , but if you stop posting problems like this for some reason you are not responsible for , we would be discouraged :(Log in to reply

– Chinmay Sangawadekar · 10 months, 3 weeks ago

I agree with you aareyan...and Nihar...Log in to reply

– Aareyan Manzoor · 10 months, 3 weeks ago

i agree; without his problem i never would have learned abt half the things iknow now, please dont stop otto sir; you are one of the best problem posters here.Log in to reply

@Otto Bretscher can you link me to some solutions like this, sorry if your experience in brilliant is harmed by them. – Aareyan Manzoor · 10 months, 3 weeks ago

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– Otto Bretscher · 10 months, 3 weeks ago

Solutions like what, Comrade?Log in to reply

these solutions posted by obnoxious guys. – Aareyan Manzoor · 10 months, 3 weeks ago

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– Otto Bretscher · 10 months, 3 weeks ago

I don't want to name names, but I think you know the type.Log in to reply

– Aareyan Manzoor · 10 months, 3 weeks ago

yes, i think i will go through your profile searching on my own for these guys.Log in to reply

– Chinmay Sangawadekar · 10 months, 3 weeks ago

Aareyan please take strict actions for people like him...Log in to reply

@Otto Bretscher – Chinmay Sangawadekar · 10 months, 3 weeks ago

I am really sorry , all this has happened because of me ...:(Log in to reply

@Chinmay Sangawadekar – Otto Bretscher · 10 months, 3 weeks ago

Not at all... you are my best Comrade here,Log in to reply

@Otto Bretscher sorry to mention you here , but in this problem , I have added 1 to the lambda function , so deno. Won't be 0 ... – Chinmay Sangawadekar · 11 months ago

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– Otto Bretscher · 11 months ago

Are we talking about the Liouville function as usual? That one takes the vales 1 and -1.Log in to reply

hi – Shuddhabho Nandi · 11 months ago

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@Otto Bretscher : Please see if it is true : We have , \(a\equiv 1\mod b\) where , \((a,b)\) are consecutive natural numbers such that , \(a> b\) , then , \(a^{n}\equiv 1\mod bn\) , this congruence is true . – Chinmay Sangawadekar · 11 months ago

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– Otto Bretscher · 11 months ago

No, this is not correct (unless I misunderstand your statement). As a counterexample, consider \(n=2, b=3, a=4\).Log in to reply

– Chinmay Sangawadekar · 11 months ago

Yeah right,,,btw also try my recent problem More Modular in 2016Log in to reply

@Abhishek Sinha , Sorry to mention you here , but I wanted to know more about the Mathematics Department of MIT Can I get in there ? What is the process to do so ? Please tell.. Also , what is your PhD topic ? – Chinmay Sangawadekar · 11 months ago

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application procedure is publicly available. I am working on Network Control and Information Theory. Good luck! – Abhishek Sinha · 11 months ago

You should apply. TheLog in to reply

@Nihar Mahajan try these problems ;) 1 , and 2 – Chinmay Sangawadekar · 11 months, 1 week ago

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@Chinmay Sangawadekar You may try this , this . – Nihar Mahajan · 11 months, 2 weeks ago

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– Chinmay Sangawadekar · 11 months, 2 weeks ago

solved ,,sorry ,, saw your comment now ,, Nice problems ..Log in to reply

@Andrew Ellinor , @Aareyan Manzoor please check this and please update the level to 5 as thos not a level 3 problem – Chinmay Sangawadekar · 11 months, 2 weeks ago

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– Andrew Ellinor · 11 months, 2 weeks ago

I've changed the level back to 3. Please let the rating system work automatically.Log in to reply

@Nihar Mahajan , you may also try this – Chinmay Sangawadekar · 11 months, 4 weeks ago

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@Nihar Mahajan , can you update my solution number ? I have written 6 and deleted my previous one so , can you do that ? or tell any staff member to do so ? – Chinmay Sangawadekar · 11 months, 4 weeks ago

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– Nihar Mahajan · 11 months, 4 weeks ago

Sorry , I can't do that , you may ask Calvin on his messageboard.Log in to reply

@Nihar Mahajan you may try this – Chinmay Sangawadekar · 11 months, 4 weeks ago

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– Nihar Mahajan · 11 months, 4 weeks ago

Thanks , I got it :)Log in to reply

@Nihar Mahajan what is the teamdomain of brilliant on slack ? – Chinmay Sangawadekar · 12 months ago

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@Nihar Mahajan , have you started learning limits ? – Chinmay Sangawadekar · 12 months ago

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– Nihar Mahajan · 12 months ago

I have finished it.Log in to reply

@Nihar Mahajan – Chinmay Sangawadekar · 12 months ago

Great What source ? M Prakash notes ?Log in to reply

– Nihar Mahajan · 12 months ago

Calculus will be done in MPA during June-July. But due to curiosity I am learning it on my own.Log in to reply

@Nihar Mahajan – Chinmay Sangawadekar · 12 months ago

Hey why dont you try and solve my NT and Algebra lvl 4-5 problems ?Log in to reply

@Chinmay Sangawadekar – Nihar Mahajan · 12 months ago

Why don't you solve my all previous problems?Log in to reply

@Nihar Mahajan – Chinmay Sangawadekar · 12 months ago

I was doing them only I did many of your recent problemsLog in to reply

@Nihar Mahajan – Chinmay Sangawadekar · 12 months ago

Hmm , so no school today for you ?Log in to reply

– Nihar Mahajan · 12 months ago

Nope, its saturday.Log in to reply

this@Nihar Mahajan – Chinmay Sangawadekar · 12 months ago

Well ,also see my level two limits problem ,Log in to reply

@Chinmay Sangawadekar – Nihar Mahajan · 12 months ago

Solved it.Log in to reply

– Chinmay Sangawadekar · 12 months ago

grt :)Log in to reply

– Nihar Mahajan · 12 months ago

Post more limit problems please, thanks :)Log in to reply

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– Nihar Mahajan · 12 months ago

Yes! If you want some limit probs even I will post it. (But they won't be original)Log in to reply

@Nihar Mahajan – Chinmay Sangawadekar · 12 months ago

okay then , btw I wanted to know how many students (Approx) from Pune get selected into top 7 IITS ? Last year from kolhapur there were only 4 , that too they were in MPA , ANd Bakliwal ... can u please tell ?Log in to reply

– Nihar Mahajan · 12 months ago

I don't know precisely though. Which academy are you joining in Pune?Log in to reply

– Chinmay Sangawadekar · 12 months ago

Yo , I Gave entrance of FIITJEE and I was qualified though , also I am going to appear for MPA . Or else ,I will be i nKOlhapur Itself ,Log in to reply

– Nihar Mahajan · 12 months ago

Also where's Shivamani joining?Log in to reply

– Chinmay Sangawadekar · 12 months ago

Me and Shivamani were thinking of joining Kota , but now Pune or Mostly SGI in kolhapurLog in to reply

– Nihar Mahajan · 12 months ago

Don't go to Kota , its not good...Log in to reply

– Nihar Mahajan · 12 months ago

Wow! Please prepare well for MPA . Its not that easy to get above 50% in its entrance.Log in to reply

– Chinmay Sangawadekar · 12 months ago

You also have to appear for MPA entrance in 11th ?Log in to reply

– Nihar Mahajan · 12 months ago

Nope , I am in MPA right from Std. 8 , so I have direct entry to 11th.Log in to reply

@Nihar Mahajan – Chinmay Sangawadekar · 12 months ago

Nice....Gotta go ,talk to you later bro , for how much time are you active now ?Log in to reply

– Nihar Mahajan · 12 months ago

Even I need to go , Talk to you later. Bye!Log in to reply

– Nihar Mahajan · 12 months ago

Yes , sure.Log in to reply

@Aareyan Manzoor see the link of problem – Chinmay Sangawadekar · 12 months ago

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@Aareyan Manzoor , @Nihar Mahajan , dont you think this is level 5 problem ?Somebody set level 3 for it. – Chinmay Sangawadekar · 12 months ago

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– Nihar Mahajan · 12 months ago

I think it must be level 3 only. Also , you must mention what \(\phi\) function is.Log in to reply

@Nihar Mahajan take a look at this I strongly feel that this problem should get level 5 (though it has no advanced concepts)atleast 200 or 195 points.Please do update the seed level.I will be very thankfull to you – Chinmay Sangawadekar · 12 months ago

HeyLog in to reply

@Chinmay Sangawadekar in the future please dont tag mods like this, if a mod comes across a problem he will change the level. By tagging you are bothering them, mods are usually busy. – Aareyan Manzoor · 12 months ago

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– Aareyan Manzoor · 12 months ago

Done. I think this is harder then the previous ones.Log in to reply

– Aareyan Manzoor · 12 months ago

It is okay. it doesnt use any hard concepts.Log in to reply

– Chinmay Sangawadekar · 12 months ago

see thishttps://brilliant.org/problems/double-polynomials/?group=3Bg9df1xnfS9&ref_id=1094417 shouldnt it be lvl 5 ???Log in to reply

@Isaac Buckley why did you choose Computer Sci. topic for this problem of yours ? – Chinmay Sangawadekar · 12 months ago

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– Isaac Buckley · 12 months ago

I didn't, I chose number theory which was then changed to computer science by a moderator. I do not contest to it, it fits well in computer science.Log in to reply

– Aareyan Manzoor · 12 months ago

Can you solve it using number theory?Log in to reply

– Isaac Buckley · 12 months ago

I'd love to see anyone try to solve it with number theory, a great prize awaits them.Log in to reply

@Isaac Buckley – Chinmay Sangawadekar · 12 months ago

Really , well is there any generelization for primes,in such form ?Log in to reply

Something you might be interesting in reading up on is Mills' constant. It's a way to find primes. It has major short comings though, still interesting. – Isaac Buckley · 12 months ago

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@Isaac Buckley – Chinmay Sangawadekar · 12 months ago

Is \(2^n - 1\) a sure prime or is it not sure for prime \(n\)?Log in to reply

– Isaac Buckley · 12 months ago

It's just a prime candidate. Try and prove that if n is composite then \(2^n-1\) is also composite.Log in to reply

– Chinmay Sangawadekar · 12 months ago

sure ,Log in to reply

– Aareyan Manzoor · 12 months ago

Only 49 n's have been found such that \(2^n-1\) iss prime..... so no!Log in to reply

– Chinmay Sangawadekar · 12 months ago

Oh thanks for that info ..Log in to reply

@Isaac Buckley – Chinmay Sangawadekar · 12 months ago

You there ?Log in to reply

– Aareyan Manzoor · 12 months ago

Yes, but mills constant is hard to use as we need to have a good degree of acuracy!Log in to reply

– Isaac Buckley · 12 months ago

Exactly! But it's still amazing that such a constant exists. It's also not known if it rational or not.Log in to reply

– Chinmay Sangawadekar · 12 months ago

Oh yes I agree with Aareyan, and thanks for the link.btw dont forget to try my problems and sorry for self advertising .;)Log in to reply

– Aareyan Manzoor · 12 months ago

It is suprising how many numbers are yet to be proven irrational. for example \(e+\pi\) is not proven to be irrational.Log in to reply

– Isaac Buckley · 12 months ago

Yeah, I love problems like that. I might actually post a problem relating to \(e+\pi\) later tonight. It came up in a past exam paper I took. If mills' constant was rational the implications could be pretty big, you could possibly (by magic) find its exact fraction and thus generate as many primes as you want.Log in to reply

– Aareyan Manzoor · 12 months ago

Cool, maybe then someone might use it to prove the riemenn hypothesis!Log in to reply

– Chinmay Sangawadekar · 12 months ago

Is it like that ?Log in to reply

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– Aareyan Manzoor · 12 months ago

The riemenn hypothesis is actually about the roots of the zeta function having only real part as 1/2. From that a the density and numbers of primes was approxomated.Log in to reply

this – Aareyan Manzoor · 12 months ago

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– Aareyan Manzoor · 12 months ago

M primes are so hard to find using comp. sci, i dont think number theory is the right approach!Log in to reply

– Chinmay Sangawadekar · 12 months ago

I dont know but problem looks like NT problem. Can you solve it by NT any tries ?Log in to reply

– Isaac Buckley · 12 months ago

I'm not going to say you can't... but if anyone could... they would be a God in the eyes of mathematicians.Log in to reply

@Isaac Buckley – Chinmay Sangawadekar · 12 months ago

Oh yeah there is no specific formats for primes iant it?Log in to reply

@Otto Bretscher , can you tell me a general formula to find the product of totient of divisors of any number n – Chinmay Sangawadekar · 1 year ago

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@Otto Bretscher , I wanted ask you about this

Does this mean , that \(n^{2015\)}=1 , ? – Chinmay Sangawadekar · 1 year ago

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– Otto Bretscher · 1 year ago

Yes, "primitive root of unity" means that 2015 is the smallest positive integer \(k\) such that \(\omega^k=1\).Log in to reply

@Chinmay Sangawadekar, lets talk about multiplicative function wiki first. – Aareyan Manzoor · 1 year ago

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– Chinmay Sangawadekar · 1 year ago

okay ,Log in to reply

here for the wiki. what level audience do we target? – Aareyan Manzoor · 1 year ago

goLog in to reply

– Chinmay Sangawadekar · 1 year ago

I think we should aim for high level audienceLog in to reply

– Aareyan Manzoor · 1 year ago

now what sections are we going to divide the wiki in?Log in to reply

– Aareyan Manzoor · 1 year ago

same in my mind. how 'bout lvl 3-5?Log in to reply

– Chinmay Sangawadekar · 1 year ago

Sure , first we will make it for level 3-4 then we will ask Calvin Lin for guidance , then we go for advanceLog in to reply

– Aareyan Manzoor · 1 year ago

ok. the sections of the wiki then... how are we going to divide it?Log in to reply

@Chinmay Sangawadekar, i see that you have interest in contributing to wikis like multiplicative functions and mobius function. talk to me at slack so we could make the wiki better. – Aareyan Manzoor · 1 year ago

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– Chinmay Sangawadekar · 1 year ago

https://crypto.stanford.edu/pbc/notes/numbertheory/mult.html , do check this out , it has many useful things which we can use for wikiLog in to reply

– Aareyan Manzoor · 1 year ago

cool, just went through it.... i was planning to include those sums....Log in to reply

– Chinmay Sangawadekar · 1 year ago

Yeah those are really awesome , so i have a plan , I will provide you with the stuff ,you select it and then tell me , then we will add those on wikiLog in to reply

– Aareyan Manzoor · 1 year ago

ok.. that is a good plan... it is going to become overcrowded your message board. try facebook. i have the same username as brilliant (aareyan manzoor).Log in to reply

– Chinmay Sangawadekar · 1 year ago

Sure I will add you immediatelyLog in to reply

@Aareyan Manzoor – Chinmay Sangawadekar · 1 year ago

Brother , I have no access to slack , when I try , it says you are already invited , but I had deleted my emails already :( is there another way to communicate ? On Facebook ?Log in to reply

here. i had the same problems.... – Aareyan Manzoor · 1 year ago

loginLog in to reply

– Dev Sharma · 1 year ago

i enter my email and pass and got Sorry, you entered an incorrect email address or password.Log in to reply

@Dev Sharma – Chinmay Sangawadekar · 1 year ago

Yeah same here ,Log in to reply

@Aareyan Manzoor – Chinmay Sangawadekar · 1 year ago

How is it ?Log in to reply

– Aareyan Manzoor · 1 year ago

oh yes that is cool... back to the topic of sections now. lets decide that what section are required for the wiki?Log in to reply

– Chinmay Sangawadekar · 1 year ago

First intro. then theorem(definition) then proof(if necessary) (examples)Log in to reply

Sorry I was practicing to make the link . The blue one... – Chinmay Sangawadekar · 1 year, 2 months ago

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– Nihar Mahajan · 1 year, 2 months ago

I wanted to spam :PLog in to reply

– Chinmay Sangawadekar · 1 year, 2 months ago

Still it is not getting the rating.Log in to reply

– Nihar Mahajan · 1 year, 2 months ago

Be patient , it will get rated as more and more people view it. If you have a valid reason for urgency for rating it , please tell .Log in to reply

Chinmay Sangawadekar – Chinmay Sangawadekar · 1 year, 2 months ago

Please as you are a moderator do check this problem.Log in to reply

– Nihar Mahajan · 1 year, 2 months ago

Formatting is alright.Log in to reply

Chinmay Sangawadekar – Chinmay Sangawadekar · 1 year, 2 months ago

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(http://shivamani patil) – Chinmay Sangawadekar · 1 year, 6 months ago

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Bonne journee is not literally used as 'good day' in francais. It's more like have a good day. Sorry to ruin it. :3

And potato or potato? – Kunal Verma · 1 year, 6 months ago

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– Chinmay Sangawadekar · 1 year, 6 months ago

Got it thanks for that bro .Actually i am learning German not frenchLog in to reply

I too have great interest in quantum physics and relativity .Keep eating carrots like Nihar because you too have the same number of letters in your name as is in carrots.I hope that you might solve the conflict of gravity and quantum mechanics in future. – Siddharth Singh · 1 year, 6 months ago

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– Chinmay Sangawadekar · 1 year, 6 months ago

which subject do you like other than mathematics and physics.Log in to reply

– Siddharth Singh · 1 year, 6 months ago

Computer Science and Astronomy.Log in to reply

– Chinmay Sangawadekar · 1 year, 6 months ago

so you want to do career in pure physics or something else?Log in to reply

– Siddharth Singh · 1 year, 6 months ago

It is very difficult for me to answer this question because of my wide range of interest in subjects of Mathematics,Physics,Computer Science and Astronomy.Log in to reply

Do you like carrots? – Agnishom Chattopadhyay · 1 year, 7 months ago

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– Chinmay Sangawadekar · 1 year, 7 months ago

yeah a little bit .what about you?Log in to reply

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– Chinmay Sangawadekar · 1 year, 7 months ago

Can anybody explain me why do many people ask the first question as do you like carrots ??Log in to reply

@Agnishom Chattopadhyay . – Nihar Mahajan · 1 year, 7 months ago

AskLog in to reply

– Chinmay Sangawadekar · 1 year, 6 months ago

did you get book on trigonometry?Log in to reply

– Nihar Mahajan · 1 year, 6 months ago

Yes I did. Thanks!Log in to reply

– Chinmay Sangawadekar · 1 year, 6 months ago

Which book should I use for advanced geometry?Log in to reply

– Chinmay Sangawadekar · 1 year, 7 months ago

Nope bro we r good friends aren't we ?Log in to reply

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– Chinmay Sangawadekar · 1 year, 7 months ago

Let it be everybody KEEP CALM AND SOLVE MY EASY ALGEBRA PROBLEM.Log in to reply

– Mehul Arora · 1 year, 7 months ago

Dude, I didn't lie :3Log in to reply

– Chinmay Sangawadekar · 1 year, 7 months ago

Arre ab jane bhi do yaarLog in to reply

Hello Everyone!!! – Chinmay Sangawadekar · 1 year, 7 months ago

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this? – Yoogottam Khandelwal · 1 year, 6 months ago

Can you help me out withLog in to reply

– Yoogottam Khandelwal · 1 year, 6 months ago

Hello!Log in to reply

– Chinmay Sangawadekar · 1 year, 6 months ago

HeyLog in to reply