SANSKAR'S OG PROBLEMS

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Hi, this page is created by ...~ SANSGANKRSNGUPTA This page contains exclusive problems made by me myself. I am the creator of these OG problems. What OG stands for is a secret! Please post your solutions with your name. If you view this page please increment the below number by one:

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Problem1

Let $\overline{ab}$ be a 2-digit positive integer satisfying $\overline{ab}^2$ = $a! +b!$. Find $a+b$ .

Problem2

For any any [positive integer] $n$, $n$>1 can $n!$ be a [perfect square]? If yes, give one such $n$. If no, then prove it.