Question Number 10062 by ridwan balatif last updated on 22/Jan/17

Commented byridwan balatif last updated on 22/Jan/17

find the remainder of the division 20^(2017) +1^(2017) +17^(2017) +72^(2017)  by 2017

Answered by nume1114 last updated on 23/Jan/17

from Fermat′s little theolem:  a^(p−1) ≡1 (mod p)  where a∈Z,p is prime.  ∴a^p ≡a (mod p)  substitute:  a=20,1,17,72 and p=2017  we get      20^(2017) +1^(2017) +17^(2017) +72^(2017)   ≡20+1+17+72(mod 2017)  =110