Originally Posted by

**jimboruss** This is my first post. I found this site when I was trying to find something online to get some help on some discrete math homework. Hopefully somebody can help me out.

I have four proofs that are the same basic type, that I just can't quite figure out. Here is an example:

(5^(n+1) + 2*3^n + 1) | 8 for all n >= {0,1,2,3,...}

here's what I have so far:

basis:

n=0 5^1 + 2*3^0 + 1 = 5 + 2 + 1 = 8 | 8 = 1

n=1 5^2 + 2*3^1 + 1 = 25 + 6 + 1 = 32 |8 = 4

so I believe the proposition is true

hypothesis: (5^(n+1) + 2*3^n + 1) | 8

going to: (5^(n+2) + 2*3^(n+1) + 1) | 8

(5^(n+2) + 2*3^(n+1) +1)

= (5*5^(n+1) + 2*3*3^n +1)

= (4*5^(n+1) + 5^(n+1) + 2*2*3^n + 2*3^n +1)

= 4(5^(n+1) + 3^n) + (5^(n + 1) +2*3^n + 1)

and this is as far as I've been able to get on all three of them.

I know that the last part (5^(n+1) + 2*3^n + 1) is divisible by 8 from the inductive hypothesis, but I can't figure out how to get the first part.

On another problem I factor out 5 from the first part but I'm trying to get it divisible by 10, and a third problem I factored out 4 trying to get it divisible by 16.

Any help would be greatly appreciated.