Four-square polynomial triples: quadratic classification and equal-degree obstructions

Mirela Jukić Bokun, Ana Jurasić

We study triples of distinct nonconstant polynomials $a,b,c$ over $\mathbb{R}$, $\mathbb{Q}$ or $\mathbb{Z}$ for which $$ab+1,ac+1,bc+1,abc+1$$ are all polyn…