Find all triples $(a, b, c)$ of positive integers such that
$a^2 + b^2 = n\cdot lcm(a, b) + n^2$
$b^2 + c^2 = n \cdot lcm(b, c) + n^2$
$c^2 + a^2 = n \cdot lcm(c, a) + n^2$
for some positive integer $n$.
Attemp: I think the only solution is $(1,1,1)$. I used FMID. Not sure of it though
I found an alleged answer: there are infinite solutions (of one parameter)