Question

Prove that 11n+2 + 122n+1 is divisible by 133

Answer 1

Answer:

First, prove it for the base case ofn=1:

11

(1+2)

+12

(2+1)

= 11

3

+12

3

= 1331+1728

= 133(10)+1+1728

=133(10)+1729

=133(10)+133(13)

=133(26)