While working on some research, I needed to find the integer solutions to the polynomial $x^4+4x^3y-6x^2y^2-4xy^3+y^4=1$. I found $(0,1)$, $(0,-1)$, $(1,0)$, $(-1,0)$, $(3,2)$, $(-3,-2)$, $(2,-3)$, $(-2,3)$. These seem to be all, but can I prove this? I factored the equation several ways. I have: $(x+y)^4-4xy^2(3x+2y)=1$, $(x-y)^4-4x^2y(3y-2x)=1$, and $x^4+2xy(2x+y)(x-2y)+y^4=1$. Any suggestions? Even if I could find some bounds for possible solutions, that would be great.
2026-03-25 06:24:56.1774419896
Integer solutions to diophantine equation $x^4+4x^3y-6x^2y^2-4xy^3+y^4=1$
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