The number 107^90 - 76^90107907690 is divisible by ?

options :-
1. 61
2. 62
3. 64
4. none of these

1 Answer
Aug 31, 2017

1. 6161

Explanation:

Given:

107^90-76^90107907690

First note that 107^9010790 is odd and 76^907690 is even.

So their difference is odd and cannot be divisible by 6262 or 6464.

To check for divisibility by 6161, let us look at powers of 107107 and 7676 modulo 6161.

107^1 -= 46107146

107^2 -= 46^2 -= 2116 -= 421072462211642

76^1 -= 1576115

76^2 -= 15^2 -= 225 -= 4276215222542

So:

107^2-76^2 -= 010727620 modulo 6161

That is 107^2-76^21072762 is divisible by 6161

Then:

107^90-76^90107907690

= (107^2-76^2)(107^88+107^86*76^2+107^84*76^4+...+76^88)

So:

107^90-76^90

is divisible by 61