Question

Determinati elementele multimii A={x € N | xy5 = 5 la x+y}

Answer 1

Puteri de 5 de trei cifre: 125, 625

$5^{x+y}=125\Rightarrow x+y=3$
$\bar{xy5}=125\Rightarrow x=1,~y=2,~x+y=3~corect$

$5^{x+y}=625\Rightarrow x+y=4$
$\bar{xy5}=625\Rightarrow x=6,~y=2,~x+y=8~fals$

x=1, y=2
$\boxed{A=\{1\}}$