A Diophantine Equation | Find Integer Solutions.

[@LilyHall-xx4do]

x=6, y=13, or x=13, y=6

[@mathsenhancersclass]

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[@martinphipps2]

If x = 6 then 216 - 30y + y^3 = 2023 so y^3 -30y -1807 = 0
so y^3 - 13y^2 + 13y^2 - 169y + 139y -1807 = 0
but 139 times 13 is 1807
so (y-13)(y^2 + 13y +139)=0
and since the original equation was symmetric in x and y we have
x=6 and y =13 or x=13 and y=6.

[@mathsenhancersclass]

Thanks