1. The problem statement, all variables and given/known data Let p be a prime and let a be an integer not divisible by p satisfying [itex] a \not \equiv 1 mod p [/itex] Show that [tex] 1 + a + a^2 + a^3 + ...... + a^p^-^2 \equiv 0 mod p [/tex] 2. Relevant equations 3. The attempt at a solution [tex] a^\phi^(^p^) = a^p^-^1 \equiv 1 mod p [/tex] [tex] a^p^-^1 -1 \equiv 0 mod p [/tex] [tex] (a^p^-^1 -1)^p \equiv 0 mod p [/tex] From a previous theorem that we did in class we showed that [itex] p [/itex] | [itex] p\choose m [/itex] [tex] a^p^(^p^-^1^) - a^p^-^1^(^p^-^1^) + ....... - a^(^p^-^1^) \equiv 0 mod p[/tex] I'm stuck here. I think I can sense that I am on the right track but I don't know which direction to go from here. Any help would be greatly appreciated!