數學知識交流---認真的XD

(1+n)^p - n^p - 1
= Σ(i=1, p-1) pCi n^i
= Σ(i=1, p-1) [p!/i!(p-i)!] n^i
Since all pCi is a positive integer, and since p is prime which means p is not divided in the fraction, therefore, pCi must be divisible by p,
Therefore, for all terms in the summation must have a factor p,

Σ(i=1, p-1) [p!/i!(p-i)!] n^i is divisible by p
=> (1+n)^p - n^p - 1 is divisible by p

[p.s. I think I may make mistake, I just gotta a try >"<""]