We study the equations , where and is a given positive integer. Except for the case (i.e., all signs are positive), which are known conjectures of Erdős–Straus (), Sierpiński () and Schinzel (), we show that the equations (with at least one minus sign) have solutions , where for sufficiently large .
"On the equations ." Rocky Mountain J. Math. 51 (2) 669 - 688, April 2021. https://doi.org/10.1216/rmj.2021.51.669