Pov L. A.

Do there exist three pairwise distinct natural numbers $a, b$, and $c$ such that the numbers $a+b+c$ and $a \cdot b \cdot c$ are squares of some natural numbers?
For example, $a=1, b=3, c=12: 1+3+12=4^{2}, 1 \cdot 3 \cdot 12=6^{2}$.

Comment. There are many other such triples. For example, if we take any Pythagorean triple $u^{2}+v^{2}=w^{2}$, then the numbers $a=u^{4}, b=v^{2} \cdot u^{2}, c=w^{2} \cdot v^{2}$ work.

## Answer

Yes.