Question

Aratati ca numarul A= 2014^15+2014^12+1 nu este numar prim.

Answer 1

$Oricare ~ar~fi~a,b,n \in N~(n \neq 0)~are~loc~relatia: \\ \\ (a+b)^n=M_a+b^n.~(M_a=multiplu~de~a) \\ \\ Deci~A=(2013+1)^{15}+(2013+1)^{12}+1=M_{2013}+1+ \\ \\ +M_{2013}+1+1=M_{2013}+3=M_{3} \Rightarrow A ~\vdots ~3 \Rightarrow A~nu~e~prim.\\ \\ \\ \\ \\ .$