Question

Determinatu ultima cifra a produsului 124×4236×78239
Determinati uktina cifra a produsului 12x14x16x.......x38

Determinati ultima cifra a nr
A) 2^8
B) 3^8
C) 5^8
D) 5^203+6^235+8^429
E) 2^2001
F) 7^2011
G)3^2011+4^2011
Determinati ultima cifra a nr 3^n+1x5^n+3^nx5^n+2+6X3^NX5^N, N=nr natural

Answer 1

Uc=ultima cifra
Uc(124×4236×78239)=Uc(4×6×9)=Uc(216)=6

Uc(12×14×16×...×38)=Uc(2×4×6×8×10×....38)=Uc(10)=0

Uc(2^8)=Uc(2^4)=6

Uc(3^8)=Uc(3^4)=1

Uc(5^8)=5

Uc(5^203+6^235+8^429)=Uc(5^203)+Uc(6^235)+Uc(8^429)=Uc(5+6+8)=
=Uc(19)=9
Uc(5^203)=5
Uc(6^235)=6
Uc(8^429)=Uc(2^1287)=Uc[2^(321×4+3)]=Uc(2^3)=8

Uc(2^2011)=Uc(2^(502×4+3)]=Uc(2^3)=8

Uc(7^2011)=Uc(7^(502×4+3)]=Uc(7^3)=3

Uc(3^2011+4^2011)=Uc(7+4)=Uc(11)=1
Uc(3^2011)=Uc[3^(502×4+3)]=Uc(3^3)=7
Uc(4^2011)=Uc[4^(1005×2+1)]=Uc(4^1)=4