A very special palindrome
Number Theory
Level
2
There exists a 3 digit palindrome such that it cal also be represented as the difference of two perfect squares, both of which are a multiple of 5. Also, the digit sum of the palindrome is even. Find this palindrome.
The answer is 525.
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1 solution
Note that if a perfect square is divisible by 5, it must end in 00 or 25. Thus, the difference must end in 00, 25 or 75. But if the number end in 00, the number must be 000, which is ridiculous. Thus, it must be either 525 or 575. The digit sum of 575 is 17 so it does not satisfy. the digit sum of 525 does satisfy. Therefore, the number is 525.
Thanks to Sharma G. for giving me this question. (No copyright infringement occurred. :P)