Interesting palindromes

Square 12. We get 144.

Reverse 12. We get 21

Square 21. We get 441

Reverse 441. We get 144.

Note by Mohmmad Farhan
3 months, 1 week ago

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  Easy Math Editor

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

\(12^2= 144 ; 21^2 = 441\)

\(122^2 = 14884; 221^2 = 48841\)

\(1222^2 = 1493284; 2221^2 = 4932841\)

Mohmmad Farhan - 1 month ago

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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.

Ram Mohith - 3 months, 1 week ago

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Make sense

Mohmmad Farhan - 3 months, 1 week ago

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

Ram Mohith - 3 months, 1 week ago

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True

Mohmmad Farhan - 3 months, 1 week ago

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

Ram Mohith - 3 months, 1 week ago

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It only works around 20

Mohmmad Farhan - 3 months, 1 week ago

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You cannot frame a question

Mohmmad Farhan - 3 months, 1 week ago

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Why can't we ?

Ram Mohith - 3 months, 1 week ago

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May I assist

Mohmmad Farhan - 3 months, 1 week ago

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

Ram Mohith - 3 months, 1 week ago

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@Ram Mohith What does periodicity mean

Mohmmad Farhan - 3 months, 1 week ago

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

Ram Mohith - 3 months, 1 week ago

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@Ram Mohith oh

Mohmmad Farhan - 3 months, 1 week ago

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Did you get still anymore numbers like these.

Ram Mohith - 3 months, 1 week ago

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@Ram Mohith There has to be some kind of error.

Mohmmad Farhan - 3 months, 1 week ago

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@Ram Mohith NO

Mohmmad Farhan - 3 months, 1 week ago

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

Mohmmad Farhan - 3 months, 1 week ago

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@Mohmmad Farhan Ok. No problem. Take your own time.

Ram Mohith - 3 months, 1 week ago

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@Ram Mohith I already updated

Mohmmad Farhan - 3 months, 1 week ago

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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.

Mohmmad Farhan - 3 months, 1 week ago

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My assumption WORKED. YAY

Mohmmad Farhan - 3 months, 1 week ago

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

Mohmmad Farhan - 3 months, 1 week ago

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AND THAT WAY WORKS

Mohmmad Farhan - 3 months, 1 week ago

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

Mohmmad Farhan - 3 months, 1 week ago

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

Ram Mohith - 2 months, 1 week ago

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

Ram Mohith - 3 months, 1 week ago

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@Ram Mohith My brother's name is Mohammad FARHAN

Mohmmad Farhan - 3 months, 1 week ago

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@Mohmmad Farhan Oh sorry for the typo.

Ram Mohith - 3 months, 1 week ago

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@Ram Mohith OK Apology accepted

Mohmmad Farhan - 3 months, 1 week ago

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

Mohmmad Farhan - 3 months, 1 week ago

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@Mohmmad Farhan P.S. I am an indian living in singapore

Mohmmad Farhan - 3 months, 1 week ago

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

Ram Mohith - 3 months, 1 week ago

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Try to find if there are any such numbers.

Ram Mohith - 3 months, 1 week ago

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Yes. It is quite good.

Ram Mohith - 3 months, 1 week ago

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This also works with \( 13 \):

\( 13^2 = 169 \)

\( 31^2 = 961 \)

Henry U - 2 weeks ago

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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 \( G81_{20} \).

Henry U - 2 weeks ago

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My friend told me that on Friday but I forgot

Mohmmad Farhan - 2 weeks ago

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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

Mohmmad Farhan - 2 months, 1 week ago

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Can you help me in my other notes

Mohmmad Farhan - 3 months, 1 week ago

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surely.

Ram Mohith - 3 months, 1 week ago

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Lets go to interesting prime powers relationship(the name)

Mohmmad Farhan - 3 months, 1 week ago

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@Mohmmad Farhan I am coming one by one.

Ram Mohith - 3 months, 1 week ago

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@Ram Mohith ok

Mohmmad Farhan - 3 months, 1 week ago

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

Mohmmad Farhan - 3 months, 1 week ago

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Unless it is a proof stating question

Mohmmad Farhan - 3 months, 1 week ago

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

Ram Mohith - 3 months, 1 week ago

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@Ram Mohith 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

Mohmmad Farhan - 3 months, 1 week ago

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@Mohmmad Farhan Yes I am also thinking about it.

Ram Mohith - 3 months, 1 week ago

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Yes. Your point is also correct.

Ram Mohith - 3 months, 1 week ago

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It only works below 20

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

Mohmmad Farhan - 3 months, 1 week ago

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Sorry. It is around 20

Mohmmad Farhan - 3 months, 1 week ago

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20 means squaring and reversing

Mohmmad Farhan - 3 months, 1 week ago

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Ok. Should see about this !!!

Ram Mohith - 3 months, 1 week ago

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WAIT 10 and 11 work

Mohmmad Farhan - 3 months, 1 week ago

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Square 20. We get 400.

Reverse 20. We get 02.

Square 02. We get 004

Reverse 400. We get 004

Mohmmad Farhan - 3 months, 1 week ago

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Good one again

Ram Mohith - 3 months, 1 week ago

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

31 times 31 = 961

and

19 times 19 = 361

Mohmmad Farhan - 3 months, 1 week ago

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