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Lost solutions of the Diophantine equation in V. 11.1

Posted 1 month ago
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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 -> -486, y -> -2}, {x -> -108, y -> -4}, {x -> -30, y -> -10}

Notice that Element[-30, Integers] returns True.

POSTED BY: Albert Lebedev

With version 13.0 I get this:

In[1]:= Solve[x (y + 1)^2 == 243 y, {x, y}, Integers]

Out[1]= {{x -> -486, y -> -2}, {x -> -108, y -> -4}, {x -> -30, 
  y -> -10}, {x -> 0, y -> 0}, {x -> 24, y -> 8}, {x -> 54, y -> 2}}
POSTED BY: Gianluca Gorni
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