Question

Use Mathematical Induction to show that 512| 8•5^n + 6•3^2n – 80n – 14 for all n E N​

Answer 1

question was updated to correct the constant term −14 (vs. −40).

We need to prove that 8(5)n+6(3)2n−80n−14 is divisible by 512 for all n∈N.

I started by taking n=1, then for n=k and then for n=k+1.