Proof by induction

1. Sep 28, 2011

guropalica

Proof by induction that 3 * 5^2n+1) + 2^3n+1 is divisible by 17!

2. Sep 28, 2011

RamaWolf

In your expression, there is an ")" without an "(" --> 3 * 5^2n+1) + 2^3n+1

so it is not clear what do to!

3. Sep 28, 2011

daveb

You also need to try yourself and let us know where you're stuck. Then we can help.

4. Sep 28, 2011

guropalica

I proved the base case n=1, and then I try doing the step case assuming that it satisfies for any k, then I try proving it by k+1.
I got sth like 24 * (3 * 5^(2k+1)) + 7 * 2^(3k +1) Now I'm stuck can't continue, I don't have any ideas :/
btw the initial equation is 3 * 5^(2n+1) + 2^(3n+1) !

5. Sep 28, 2011

guropalica

Got it now :) let's denote the initial statement as K + L, so we have sth like 24l + 7k = 7(k+l) + 17k, sum of two numbers divisible by 17 is divisible by 17, anyway thx