Question

Aratati ca suma a 2016 numere care dau acelasi rest prin impartire la 2016 se impart exact la 2016 .
VA ROG MULT , DAU CORONITA !!!

Answer 1

a₁:2016=b₁ rest c⇒a₁=2016b₁+c
a₂:2016=b₂ rest c⇒a₂=2016b₂+c
.........................
an:2016=bn rest c⇒an=2016bn+c
(a₁+a₂+....+an):2016=(2016b₁+c+2016b₂+c+...+2016bn+c):2016,observam ca avem 2016 de c deoarece avem 2016 de numere.
deci (a₁+a₂+...+an):2016=(2016b1+2016b2+......+2016bn+2016c):2016=2016(b1+b2+...+bn+c):2016=b₁+b₂+...+bn+c ceea ce inseamna rest 0.