Alright, here is the problem:
using the principle of mathematical induction prove that, for any positive integer n,
n^4 + (n+1)^4 + (n+2)^4 + (n+3)^4 + 14 is divisible by 16.
What I have done so far is the base step, and I have assumed the statement is true for n=k.
For n=k+1 I have added (k+4)^4 - k^4 to the expression for n=k. Once I came up with that equation, I expanded all the parts...
I ended up with 4k^4 + 40k^3 + 180k^2 + 400k + 368
now I have no idea where to go with it...
thank-you in advance for any help.