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### palindrome number

Posted: Sat Feb 04, 2012 7:58 pm
prove that, there exits no palindrome number of 2 digit which is a perfect square.no trial & error,plz.try to prove with logic.

### Re: palindrome number

Posted: Sun Feb 05, 2012 4:13 pm
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.

### Re: palindrome number

Posted: Fri Feb 17, 2012 4:21 pm
number 23. Reverse and add that number to 23 to yield the palindrome 55.

### Re: palindrome number

Posted: Sat Feb 18, 2012 3:59 pm
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.

### Re: palindrome number

Posted: Fri Jan 25, 2013 10:19 pm
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.

### Re: palindrome number

Posted: Sat Jan 26, 2013 12:16 am
Prosenjit,
Your solution is close to brute force.you have to show that 11 must divide them.Eventually in order to be a perfect square 121 must divide them.Which is not possible.