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Let $n$ be a positive integer. We study the diophantine equation$ab(ab-1)-na=\Delta^2$, where $a,b$ are positive integers. We also show that ifa system of two congruences is soluble, then an equation which is a translationof Erd\H{o}s-Straus conjecture is soluble.

On the equation $ab(ab-1)-na=\Delta^2$