The number 107^90 - 76^9010790−7690 is divisible by ?
options :-
1. 61
2. 62
3. 64
4. none of these
options :-
1. 61
2. 62
3. 64
4. none of these
1 Answer
Aug 31, 2017
1.
Explanation:
Given:
107^90-76^9010790−7690
First note that
So their difference is odd and cannot be divisible by
To check for divisibility by
107^1 -= 461071≡46
107^2 -= 46^2 -= 2116 -= 421072≡462≡2116≡42
76^1 -= 15761≡15
76^2 -= 15^2 -= 225 -= 42762≡152≡225≡42
So:
107^2-76^2 -= 01072−762≡0 modulo6161
That is
Then:
107^90-76^9010790−7690
= (107^2-76^2)(107^88+107^86*76^2+107^84*76^4+...+76^88)
So:
107^90-76^90
is divisible by