Four squares from three real polynomials

Ana Jurasić

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arXiv · 2607.06586

Four squares from three real polynomials

Ana Jurasić

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Abstract

We construct three nonconstant polynomials $a,b,c\in \mathbb{R}[X]$ such that \[ab+1,\qquad ac+1,\qquad bc+1,\qquad abc+1 \] are all squares in $\mathbb{R}[X]$. The entries in the construction are quadratic, so the construction has the smallest possible positive degrees. By composition with nonconstant polynomials, this gives infinitely many examples over $\mathbb{R}[X]$ with all entries nonconstant.

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Ana Jurasić. 2026-07-05. Four squares from three real polynomials. https://arxiv.org/abs/2607.06586

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