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**1. 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]

**2. Homework 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!

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