Question

aratati ca numarul N=1986^1986+1987^1987+1988^1988 este divizibil cu 5

Answer 1

N=1986^1986+1987^1987+1988^1988

Uc(1986^1986)=Uc(6^1986)=6
Uc(1987^1987)=Uc[7^(496*4+3)]=Uc(7^3)=Uc(343)=3
Uc(1988^1988)=Uc[8^(497*4)]=Uc(8^4)=Uc(4096)=6

Uc(N)=Uc(1986^1986+1987^1987+1988^1988)=Uc(6+3+6)=Uc(15)=5
deci este divizibil cu 5