Proving Divisibility by 9 using Induction

[holezch]

Homework Statement

prove that for all n>0 , 4^n + 15n - 1 is divisible by 9/multiple of 9

Homework Equations

The Attempt at a Solution

need to show: 4^(n+1) + 15(n+1) + 14/9 = a*k a and k are integers
assumption to inductive step: (4^n + 15n - 1)/9 = k --> 4^n + 15n - 1 = 9k -->
4^n+1 + 60n - 4 = 36k.. now what? I tried 4^n+1 -4 = 6(6k - 10n) but ultimately , I am stuck

please help! tank you

 

[Avodyne]

need to show: 4^(n+1) + 15n + 14/9 = a*k a and k are integers

Where did you get this?

Let f(n) = 4^n + 15n - 1. First, you need to show that f(1) is divisible by 9. Then, you need to show that f(n+1) is divisible by 9 if f(n) is.

 

[holezch]

sorry , I had a typo. thanks for the reply but I got the answer!