Question

Aratati ca :
$15 {}^{n + 1} + 3 {}^{n} \times 5 {}^{n + 1 } - 3 {}^{n + 2} \times 5 ^{n} se \: imparte$
exact la 165


va rog dau coroana​

Answer 1

$(3\cdot5)^{n+1}+3^n\cdot5^{n+1}-3^{n+2}\cdot5^n=3\cdot3^n\cdot5\cdot5^n+3^n\cdot5\cdot5^n-3^2\cdot3^n\cdot5^n=3^n\cdot5^n(3\cdot5+5-9)=11\cdot15^n$

$165|11\cdot15^n\\165=11\cdot15 \implies 15|15^n, Adevarat$