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Claim. N. A. Carella, Squarefree Values Of Polynomials, arXiv:2310.16952v1 (25 October 2023, math.GM). Its Theorems 1.1, 1.2 and 1.3 claim that each of the quartics $T^4+1$, $T^4+2$ and $T^4-2T^2+2$ takes infinitely many squarefree values, with an asymptotic formula $c_f x+O(x^{1/2+\varepsilon})$ for the number of squarefree values at $x\le n\le2x$. Theorem 1.2 is the case $n^4+2$ that Problem 978 names, which the preprint describes as an open question.

Covers. The third question of Problem 978, claimed yes. The three quartics are also degree-$4$ instances of the second question, at exponent $k-2=2$.

Read depth. The statements of Theorems 1.1--1.3 are read in the arXiv version; the proofs are not checked here.

Standing. The preprint has no journal reference and no outside review is recorded, so the claim stays claimed. The release manuscript carded as OpenAI 2026 cites the preprint and does not use it as an input; the third question is settled by OpenAI's density theorem.

Depends on. No page of this wiki.