Question

Using P.M.I prove that 11^n+2+12^2n+1 is divisible by 133 for all n€N

Answer 1

Answers : (1)

True for k: 11^(n+2) + 12^(2n+1) = 133(m), where m is an integer. The stuff in the parentheses will be an integer, so the result is a multiple of 133. Therefore by induction a number of that form is divisible by 133.