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Mathematica version 11.1. The input Solve[x (y + 1)^2 == 243 y, {x, y}, Integers] yields the set of solutions {{x -> 24, y -> 8}, {x -> 54, y -> 2}, {x -> 0, y -> 0}} but there are also other solutions with negative x,y: {x...
Thank you very much for the explanation!