Question 42
Determine all triples of strictly positive integers $(a,b,c)$ such that
- $a\le b\le c$;
- $\gcd(a,b,c)=1$;
- $a$ divides $b+c$, $b$ divides $c+a$, and $c$ divides $a+b$.
- $a\le b\le c$;
- $\gcd(a,b,c)=1$;
- $a$ divides $b+c$, $b$ divides $c+a$, and $c$ divides $a+b$.