Question

Aflați ultima cifra a nr: a = 2^2001 + 3^2001+4^2001+5^2001+6^2001+7^2001

Answer 1

Răspuns:

Notam ultima cifra a numarului a cu U(a):

$U(a)=U(2^{2001}) +U(3^{2001})+U(4^{2001}) +U(5^{2001}) +U(6^{2001}) +U(7^{2001})\\ U(a)=U(2^{...1}) +U(3^{...1})+U(4^...1}) +U(5^{...1}) +U(6^{...1}) +U(7^{...1})\\U(a)=U(2)+U(3)+U(4)+U(5)+U(6)+U(7)\\U(a)= U(27)=7$