pow:problem4s22 [Department of Mathematics and Statistics, Binghamton University]

Problem 4 (due on Monday, March 28)

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 Solution.