Oh wow thanks, that was totally not intuitive for me for some reason, but I see it much more clearly now. I just started doing modular arithmetic and never realized the same rules still apply. I guess "≡ (mod n)" is the same as "=" as far as any calculations are concerned?
I have a simple question:
Why does 8^7 ≡ (-5)^7 (mod 13) and (25)^3 ≡ (-1)^3 (mod 13)?
In essence I want to show that 8^7 + 5^7 = 13^7, so that both sides of the equation ≡ 0 (mod 13) and therefore 8^7 ≡ (-5)^7 (mod 13).
I know that in a field of characteristic p>0, (x + y)^p = x^p +...