Question

Fie E=5^n+2+5^n+1-5^n, arătați ca:
E divizibil 145​

Answer 1

$E=5^{n+2}+5^{n+1}-5^n\\ \\ E=5^{n}(5^2+5-1)\\ \\ E=5^n(25+5-1)\\ \\ E=5^n\cdot 29\\ \\ E=5^{n-1}\cdot 5\cdot 29\\ \\ E=5^{n-1}\cdot 145 \ \vdots \ 5 \ oricare \ ar \ fi \ n \in \mathbb{N^*}$