Question 38
Find all triplets $\{a, b, c\}$ of coprime positive integers (not necessarily pairwise coprime) such that $a+b+c$ divides simultaneously the three numbers $a^{12}+b^{12}+c^{12}$, $a^{23}+b^{23}+c^{23}$, and $a^{11004}+b^{11004}+c^{11004}$.