Question

Aratati ca 9^1996-7^1992 e divizibil cu 10.

Answer 1

Vom determina ultima cifră a fiecărui termen.

$\it u(9^{1996}) = u(9^2)^{998} =u(81)^{998} = u(1^{998}) =1 \\ \\ u(7^{1992}) u(7^4)^{498} = u(2401)^{498} = u(1^{498}) = 1 \\ \\ u(9^{1996} -7^{1992} ) = 1-1 = 0 \Rightarrow (9^{1996} -7^{1992}) \ \vdots\ 10$