This was a wonderful question given to me by professor in my last class test. He asked for the solution with the least number of steps.
Find the number of integral solutions $(x,y)$ of the equation:
$$x^3+3x^2y+3xy^2+2y^3=50653$$
Can anyone do it?
2026-04-12 23:12:06.1776035526
The number of integral solutions $(x,y)$ of $x^3+3x^2y+3xy^2+2y^3=50653$
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Note that this is $$ (x + y)^3 + y^3 = 37^3; $$ by Wiles' theorem the only integral solutions are $(37,0)$ and $(-37,37)$.