Question

calculati ultima cifra a numarului N=2007 la puterea 2000 si stabiliti daca este patrat perfect

Answer 1

U(N)=U(2007^2000)=U(7^2000)
U(7^1)=7
U(7^2)=9
U(7^3)=3
U(7^4)=1
U(7^5)=7
.................
2000:4=500 (rest 0)

Am impartit la 4 ptr ca U(7^n) poate fi 7, 9, 3 sau 1

U(7^2000)=U(7^{4×500+0} )=U(7^4)=1

R: U(N)=1



N=2007^2000=2007^(2·1000)=(2007^1000)^2 => e patrat perfect




Nota: " ^ " inseamna " la puterea..."