Question

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Answer 1

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Answer 2

First of all :

Grouping of terms :

$1^{1997} + 2^{1997} + ................ 1996^{1997}\\\\\implies 1^{1997}+1996^{1997}+2^{1997}+1995^{1997}+........$

This is very interesting .

As a class 10 boy , I will not do it complexly .

$a^n+b^n$ is always divisible by a + b when n is odd.

Obviously n = 1997 is odd .

$a^n+b^n$ is divisible by 1996 + 1 = 1997.

So every number in the series is divisible by 1997 .

Hence we proved it.