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Max Alekseyev
Max Alekseyev
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It can be reduced to Mordell equation: $$Y^2 = X^3 + (4ABC)^2$$ with $Y:=4AB(2By^3-C)$ and $X:=-4ABxy$, which was shown by Mordell to have finitely many integer solutions.

ADDED. M. A. Bennett and A. Ghadermarzi (2015) explored the connection between Mordell equations and cubic Thue equations, and computed all solutions for the former with the free terms below $10^7$ by absolute value.

It can be reduced to Mordell equation: $$Y^2 = X^3 + (4ABC)^2$$ with $Y:=4AB(2By^3-C)$ and $X:=-4ABxy$, which was shown by Mordell to have finitely many integer solutions.

It can be reduced to Mordell equation: $$Y^2 = X^3 + (4ABC)^2$$ with $Y:=4AB(2By^3-C)$ and $X:=-4ABxy$, which was shown by Mordell to have finitely many integer solutions.

ADDED. M. A. Bennett and A. Ghadermarzi (2015) explored the connection between Mordell equations and cubic Thue equations, and computed all solutions for the former with the free terms below $10^7$ by absolute value.

Source Link
Max Alekseyev
Max Alekseyev
  • 34.3k
  • 5
  • 74
  • 152

It can be reduced to Mordell equation: $$Y^2 = X^3 + (4ABC)^2$$ with $Y:=4AB(2By^3-C)$ and $X:=-4ABxy$, which was shown by Mordell to have finitely many integer solutions.