Difference between revisions of "SANSKAR'S OG PROBLEMS"

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Let <math>\overline{ab}</math> be a 2-digit [[positive integer]] satisfying <math>\overline{ab}^2</math> = <math>a! +b!</math>. Find <math>a+b</math> .
 
Let <math>\overline{ab}</math> be a 2-digit [[positive integer]] satisfying <math>\overline{ab}^2</math> = <math>a! +b!</math>. Find <math>a+b</math> .
 
==Problem2 ==
 
==Problem2 ==
For any any [[positive integer]] <math>n</math>, <math>n</math>>1 can <math>n!</math> be a [[perfect square]]? If yes, give one such <math>n</math>. If no, then prove it.
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For any [[positive integer]] <math>n</math>, <math>n</math>>1 can <math>n!</math> be a [[perfect square]]? If yes, give one such <math>n</math>. If no, then prove it.

Revision as of 08:25, 18 January 2024

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