`1 1^(n+2)+1 2^(2n+1)` is divisible by 133.

Prove the following by using the principle of mathematical induction for all n in N 11^(n+2)+ 12^(2n+1) is divisible by 133.

11^(n+2)+12^(2n+1) is divisible by 133

Prove by mathematical induction that (11^(n+2)+12^(2n+1)) is divisible by 133 for all non-negative integers.

10^(2n-1)+1 is divisible by 11.

By Mathematical Induction, prove the following: (i) (4^(n) + 15n - 1) is divisible by 9, (ii) (12^(n) + 25^(n – 1)) is divisible by 13 (iii) 11^((n + 2)) + 12^((2n + 1)) is divisible by 133 for all ninN