# Interesting palindromes

Square 12. We get 144.

Reverse 12. We get 21

Square 21. We get 441

Reverse 441. We get 144.

2 years, 6 months ago

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@Ram Mohith, There is a problem that goes something like this

$12^2= 144 ; 21^2 = 441$

$122^2 = 14884; 221^2 = 48841$

$1222^2 = 1493284; 2221^2 = 4932841$

- 2 years, 4 months ago

Yes. It is quite good.

- 2 years, 6 months ago

Try to find if there are any such numbers.

- 2 years, 6 months ago

Well I noticed that the 144 is 12 squared. And the prime factorization of 144 is 3^2 times 2^4 which is 4^2 and 3 and 4 are consecutive.

- 2 years, 6 months ago

AND THAT WAY WORKS

- 2 years, 6 months ago

Yes that is a good way finding such numbers. I too will try.

- 2 years, 6 months ago

P.S. I am 10 this my Brother's account

- 2 years, 6 months ago

P.S. I am an indian living in singapore

- 2 years, 6 months ago

So your brother name is Mohammad Farhan. How come at the age of 10 you came to know all about these.

- 2 years, 6 months ago

Well, I find school outdated that is why I check up all of this and learn and ask from my father

- 2 years, 6 months ago

My brother's name is Mohammad FARHAN

- 2 years, 6 months ago

Oh sorry for the typo.

- 2 years, 6 months ago

OK Apology accepted

- 2 years, 6 months ago

Once check my profile. I have changed my quotation. It is quite interesting and yet it has quite depth meaning in it.

- 2 years, 6 months ago

You just take two consecutive numbers. Then multiply them. and then the rest works.

- 2 years, 6 months ago

My assumption WORKED. YAY

- 2 years, 6 months ago

I am thinking to frame a question based on these observations.

- 2 years, 6 months ago

May I assist

- 2 years, 6 months ago

Did you get still anymore numbers like these.

- 2 years, 6 months ago

I am currently doing courses. Give me a minute and I will update you

- 2 years, 6 months ago

Ok. No problem. Take your own time.

- 2 years, 6 months ago

- 2 years, 6 months ago

NO

- 2 years, 6 months ago

There has to be some kind of error.

- 2 years, 6 months ago

I am trying to obtain a general form for these numbers or if there is some periodicity between the numbers .

- 2 years, 6 months ago

What does periodicity mean

- 2 years, 6 months ago

Like there is some common difference between the numbers. More clearly they should be in any progression or series.

- 2 years, 6 months ago

oh

- 2 years, 6 months ago

You cannot frame a question

- 2 years, 6 months ago

Why can't we ?

- 2 years, 6 months ago

It only works around 20

- 2 years, 6 months ago

All single digit integers will satisfy this condition the reason being when they are reversed the same number is obtained.

- 2 years, 6 months ago

True

- 2 years, 6 months ago

All multiples of 10 are exceptions to this condition. Reason :

$10^2 = 100$. On reversing 10 we get $01$. Now square it we get $01^2 = 1 = 01 = 001 = 0001 ..... and~so~on$. Now reversing it we get $10,100,1000 .....and~so~on$. So, the multiples of $10$ are exceptions. More clearly they will be in an undetermined form.

- 2 years, 6 months ago

Make sense

- 2 years, 6 months ago

This also works with $13$:

$13^2 = 169$

$31^2 = 961$

- 2 years, 4 months ago

My friend told me that on Friday but I forgot

- 2 years, 4 months ago

And if you take $14$ in base $20$ (so 24 in base 10) and square it, you get $18G_{20}$. If you square $42_{20}$ (81 in base 10) you get $G81_{20}$.

- 2 years, 4 months ago

Did you know that both the endings of 31 and 19 end in 61.

31 times 31 = 961

and

19 times 19 = 361

- 2 years, 6 months ago

Square 20. We get 400.

Reverse 20. We get 02.

Square 02. We get 004

Reverse 400. We get 004

- 2 years, 6 months ago

Good one again

- 2 years, 6 months ago

It only works below 20

EDIT: The pattern is with 1 and a followed number of 2's

- 2 years, 6 months ago

- 2 years, 6 months ago

WAIT 10 and 11 work

- 2 years, 6 months ago

Sorry. It is around 20

- 2 years, 6 months ago

20 means squaring and reversing

- 2 years, 6 months ago

The idea of making a problem out of this out of question

- 2 years, 6 months ago

Unless it is a proof stating question

- 2 years, 6 months ago

Yes. Your point is also correct.

- 2 years, 6 months ago

But my idea is not to write a proof based question.

- 2 years, 6 months ago

You can twist the question in the direction of palindromes. Say you give examples for palindromes and ask whether it works all the time ( For other numbers too). And you give three options. Yes, always , No, never and Yes , sometimes. But do not make it too obvious

- 2 years, 6 months ago

Yes I am also thinking about it.

- 2 years, 6 months ago

Can you help me in my other notes

- 2 years, 6 months ago

surely.

- 2 years, 6 months ago

Lets go to interesting prime powers relationship(the name)

- 2 years, 6 months ago

I am coming one by one.

- 2 years, 6 months ago

ok

- 2 years, 6 months ago

There is a question on this (but I forgot and cannot search). The real pattern is 1 followed by some number of 2's and when you reverse it still makes sense

- 2 years, 6 months ago