## palindrome number

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MATHPRITOM
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### palindrome number

prove that, there exits no palindrome number of 2 digit which is a perfect square.no trial & error,plz.try to prove with logic.

nafistiham
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### Re: palindrome number

all the two digit palindromes are $10k+k=11k$ type. where $k$ can be $1,2,3,4,5,6,7,8,9$ but if $11k=p^2$ $11$ must divide $k$. which it does not.so it isn't possible.
$\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0$
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qeemat
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### Re: palindrome number

number 23. Reverse and add that number to 23 to yield the palindrome 55.

nafistiham
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### Re: palindrome number

qeemat wrote:number 23. Reverse and add that number to 23 to yield the palindrome 55.
sorry,but i am a little confused what are you trying to say. the condition says to find a two digit palindrome square.
$\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0$
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.

Prosenjit Basak
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Joined: Wed Nov 28, 2012 12:48 pm

### Re: palindrome number

The palindromes of two digits always have the same digit .So there are $9$ palindromes of two digit number. If there remains a perfect square palindrome,its first digit must be $1,4,5,6,9$ .So the palindromes must be $11,44,55,66,99$ .But neither of them is perfect square.So there doesn't exist any palindrome perfect square. Yesterday is past, tomorrow is a mystery but today is a gift.