Please help me prove this equation.
Let p be a prime number and let a,b be any integers. Prove that (a+b)^p =a^p+b^p (mod p).
Maths question
2008-10-08 2:38 pm
回答 (1)
2008-10-08 6:43 pm
✔ 最佳答案
Using the binomial theorem (see for example: http://en.wikipedia.org/wiki/Binomial_theorem)(a+b)^p
=sum((p,k)a^(p-k)b^k) over k
where
(p,k)=p!/(k!(p-k)!)
if p is prime, then mod(p,k)=0 except k=0 and k=p where (p,k)=1.
Thus the summation simplifies to
(a+b)^p mod(p) = (a^p+b^p) mod(p)
收錄日期: 2021-04-13 16:09:44
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