1. The problem statement, all variables and given/known data Compute: [tex](a + b)^5[/tex] in Z_5 (Z mod 5). 2. Relevant equations The end result is apparently: [tex](a^5 + b^5)[/tex] Intuition would tell me to exploit the properties of arithmetic in Z_n, however I don't see how I can reconcile this solution with just a normal expansion of (a+b)^5 (which seems to be allowed due to the def. of arithmetic for these classes.) 3. The attempt at a solution Well, my best guess would be to show that the middle terms go to zero no matter what. But trying this with for example (a+b)^2 (which has the analagous sol'n) would mean that ab + ba = ab + ab = 0 (mod 5). However, choosing for example a = , and b = , shows that this would actually be + =  = , which clearly is not 0... so I'm at a loss. or.. I could have read this question wrong.. or perhaps my world view of modular arithmetic is one big illusion. ugh.