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a fost răspuns

Calculati ultima cifra a numarului : 16^2006 + 17^2007 + 18^2008 + 19^2009 + 20^2010 . 

Răspuns :

[tex]u(16^{2006}+17^{2007}+18^{2008}+19^{2009}+20^{2010})= \\ u[u(6^{2006})+u(7^{2007})+u(8^{2008})+u(9^{2009})+u(0^{2006})]= \\ u(6^{2006})=6~pt.~ca:\\ u(6^1)=6;~u(6^2)=6;~u(6^3)=6 \\ u(7^{2007})=3~pt.~ca:\\ 2007:4=501~r~3;~u(7^3)=3 \\ u(8^{2008})= 0~pt.~ca:\\ 2008:4=502~r~0;~u(7^0)=1 \\ u(9^{2009})=9~pt.ca:\\ 2009:4=502~r~1;~u(9^1)=9 \\ u(0^{2006})=0 \\ u(6+3+1+9+0)=u(19)=9[/tex]