Question

Aratati ca 35+7^2016 este divizibil cu 42

Answer 1

[tex]35+7^{2016}=7\cdot 5+7\cdot 7^{2015}=7(5+7^{2015})=7[5+(6+1)^{2015}]=\\ =7(5+M_6+1)=7(6+M_6)=42(1+M_6) \vdots 42\\ Am\ folosit\ formula:\boxed{(a+b)^n=M_a+b^n}[/tex]