Question

1. Aratati ca b=(5^62+5^61+5^60)*961 este un cub perfect.

Answer 1

    
[tex]961 = 31^2 \\ b=(5^{62}+5^{61}+5^{60}) \times 961 = \\ = 5^{60}(5^2+5^1+5^0) \times 31^2 = \\ = 5^{20 \times 3}(25+5+1) \times 31^2 = \\ = (5^{20})^3 \times 31 \times 31^2 = \\ =(5^{20})^3 \times 31^3 = \\ = \boxed{(5^{20} \times 31)^3 = cub~perfect }[/tex]