Proof by Induction: Divisibility by 17

[guropalica]

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

 

[RamaWolf]

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

so it is not clear what do to!

 

[daveb]

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

 

[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) !

 

[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