Abstract
In this note, we consider the Erdős–Straus Diophantine equation
where n and c are positive integers with \(\gcd (n, c) = 1\). We provide a formula for the number f(n, c) of all positive integral solutions (x, y, z) of the equation. In 1948, Erdős and Straus conjectured that \(f(n,4) \ge 1,\) for all integers \(n \ge 2\). Here, we solve the conjecture for a special case of n.
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The authors express their gratitude to the referee for the constructive suggestions on an earlier draft of this paper.
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Subburam, S., Togbé, A. A note on the Erdős–Straus conjecture. Period Math Hung 72, 43–49 (2016). https://doi.org/10.1007/s10998-015-0109-9
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DOI: https://doi.org/10.1007/s10998-015-0109-9