Question

calculati ultima cifra a puterior 4^2015 ; 7^2015, 8^2015

Answer 1

[tex]U(4^{2015})=U(4^{2*1007+1})=U(4^{1})=4\\ U(7^{2015})=U(7^{4*503+3})=U(7^{3})=U(343)=3\\ U(8^{2015})=U(8^{4*503+3})=U(8^{3})=U(512)=2[/tex]

Answer 2

4^2015

4^1=4
4^2=16
4^3=64 (se repeta ultima cifra)

Sunt doua terminații posibile:
2015:2=1007 rest 1

u (4^2015)=u (4^1)=4


7^2015

7^1=7
7^2=49
7^3=...3
7^4=...1
7^5=...7 (se repeta ultima cifra)

4 terminații posibile
2015:4=503 rest 3

u (7^2015)=u (7^3)=3


8^2015

8^1=8
8^2=64
8^3=...2
8^4=...6
8^5=...8 (se repeta ultima cifra)

4 terminații posibile
2015:4=503 rest 3

u (8^2015)=u (8^3)=2