On the equation $ab(ab-1)-na=Δ^2$

preprint2019arXivOpen access

Let $n$ be a positive integer. We study the diophantine equation $ab(ab-1)-na=Δ^2$ , where $a,b$ are positive integers. We also show that if a system of two congruences is soluble, then an equation which is a translation of Erdős-Straus conjecture is soluble.

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On the equation $ab(ab-1)-na=Δ^2$

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On the equation ab(ab−1)−na=Δ2ab(ab-1)-na=Δ^2ab(ab−1)−na=Δ2

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On the equation $ab(ab-1)-na=Δ^2$