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This is related to my first MO question and Kevin Buzzard's conjecture at Integers not represented by $ 2 x^2 + x y + 3 y^2 + z^3 - z $

This is related to my first MO question and Kevin Buzzard's conjecture at Integers not represented by $ 2 x^2 + x y + 3 y^2 + z^3 - z $

Monday, August 20: A student of Kevin Buzzard, in what would be a Master's thesis in the U.S., proved that for any integers $A,B,$ both the inhomogeneous polynomials $$ x^2 + x y + 6 y^2 + z^3 + A z^2 + B z $$ and $$ x^2 + x y + 8 y^2 + z^3 + A z^2 + B z $$ are universal, they integrally represent all integers. He also did a fixed one, $$ 2x^2 + x y + 2 y^2 + z^3 + z. $$ So the hard case really is these non-universal ones.