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BrandonMYates/yz-cubic-comparator

Brandon Yates

Palomar Registrypalomar/PALOMAR-2026-08-27-000010Aug 27, 2026math.NTscore 0

This project formalizes in Lean 4 the statement that the Diophantine equation y*z*(y+z) = x^3 + x^2 + 3x - 1 admits no polynomial parametrization over the rationals whose x-coordinate has degree between 1 and 4. Writing f = X^3 + X^2 + 3X - 1, the compared theorem is that there is no triple of rational polynomials (g, u, v) with g nonconstant of degree at most 4 satisfying the identity u*v*(u+v) = f composed with g. Exhibiting such a family is one of the two standard ways an equation of this shape is settled affirmatively -- the other being a sporadic solution -- and the theorem closes that…

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