Question

2la puterea 111 + 3 la puterea 222+4 la puterea 333+...+9 la puterea 888 divizibil cu 5

Answer 1

Uc(2^111)=Uc(2^27*4+3)=Uc(2^3)=8
Uc(3^222)=Uc(3^55*4+2)=Uc(3^2)=9
Uc(4^333)=Uc(4^166*2+1)=Uc(3^2)=4
Uc(5^444)=5
Uc(6^555)=6
Uc(7^666)=Uc(7^166*4+2)=Uc(7^2)=Uc(49)=9
Uc(8^777)=Uc(8^194*4+1)=Uc(8^1)=8
Uc(9^888)=Uc(9^444*2)=Uc(9^2)=1
Uc(2^111+3^222+4^333+5^444+6^555+7^666+8^777+9^888)=
=(Uc(8+9+4+5+6+9+8+1)=Uc(50)=0  deci divizibil cu 5