The reason I had done this was not with respect to the proof, but because it made it easier for me to test whether or not this is actually divisible by 30 (my professor wants us to be in the habit of testing things and not just taking his word that they are true). Thank you for your help though.
I was given the assignment
"Show that for all integers a and b, ab(a^2 -b^2)(a^2 +b^2) is divisible by 30."
Now, I am aware that this fails if a=b, but I want to try to prove this if we assume a≠b.
I've reduced it to the equation (a^5)b-a(b^5), which works, and I know that I could pick the...
Wouldn't this not work if a=1 then? Because then a -1 = 1 -1 = 0 and a^n - 1 = 1^n - 1 = 1 - 1 = 0. So you would always be trying to divide 0 by 0, which is undefined.
Homework Statement
Prove that if a is in Z (if a is an integer), then for every positive integer n, a-1 divides a^n -1.
Homework Equations
The Attempt at a Solution
I'm really not entirely sure where to start with this one. Can someone help?