## number theory problem

1. The problem statement, all variables and given/known data
Prove that

$$\frac{1}{p} c(p,n) = (-1)^{n-1}/n (mod p)$$

I expanded that combination in every way I could think and I tried to use Wilson's Theorem and I couldn't get :(

2. Relevant equations

3. The attempt at a solution
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 Recognitions: Homework Help Science Advisor That's p choose n, right? Try writing the LHS out as a fraction with the stuff in the numerator as negative representatives. It should nicely cancel to give the result.
 What do you mean "negative representatives"?

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## number theory problem

-(p-1)/2, -(p-2)/2,..., -1 for odd p
 Recognitions: Homework Help Science Advisor What is 1/n, or -1/n mod p supposed to mean?

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Homework Help
 What does OP stand for? Is that me? I just realized that my book my book defines congruence as $$x \equiv y \mod p$$ when x-y is a rational number whose numerator, in reduced form, is divisible by p. So, it is like a generalized congruence or something... Are there different rules for these generalized congruences? I am not sure why what Gokul43201 wrote cancels nicely?