Aflati ultima cifra a numarului a=5 la puterea 2020+1×2×3×...×2019+2×3

a=[tex]5^{2010}+1*2**...*2019+2*3[/tex]=[tex]5^{2010}+1*2**...*2019+6[/tex]

Fie x=[tex]5^{2010}[/tex]

y=[tex]1*2**...*2019[/tex]

z=6

Se noteaza U(m) ultima cifra a nr m.

U(x)=5(5 la orice putere se termina in 5)

U(y)=0(de la 5! incolo toate factorialele se termina in 0)

U(z)=6

deci U(a)=U(5+0+6)=U(11)=1