Find all triples $(a, b, c) \in \mathbb{R} : ab + c = bc + a = ca + b = 4$ Any help on this question would be great. Ive found that (1,1,3), (3,1,1), (1,3,1) but am confused on how to find more anymore (if there are any).Any help would be appreciated.

If $ab+c=bc+a$ then $ab-bc+c-a=0$ that is $(a-c)(b-1)=0$.
Thus $a=c$ or $b=1$. Similarly $a=b$ or $c=1$. Also $b=c$ or $a=1$.
Combining these we get various cases to consider. For instance,
if $a=c$ and $a=b$ then $4=a^2+a$ etc. Or if $a=c$ and $c=1$ then
$4=ac+b=1+b$ so $b=3$ etc.
