The number $N=\frac{1}{2}ab(a^4+b^4)$, where $a,b$ are positive integers such that \[ a^4+b^4=1+ab(1+2+3+\ldots +(a+b)).\] What is $N$? We have not received any solutions. The number $N=2022$. For a complete solution see the following link {{:pow:2022sproblem4.pdf|Solution}}.