- #1
Ed Aboud
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Homework Statement
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]
Homework Equations
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!
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