Freshman's Dream

Lesson · Advanced

Number Theory: Modular Arithmetic

If p is prime, then

(a+b)^p\equiv a^p+b^p\pmod p

More generally

(a_1+a_2+\cdots+a_n)^p\equiv a_1^p+a_2^p+\cdots+a_n^p\pmod p

For every positive integer k

(a+b)^{p^k}\equiv a^{p^k}+b^{p^k}\pmod p