Claims

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1950_01_01_oblath: Obláth's refereed result (Publ. Math. Debrecen 1950) that the product of five consecutive terms of a coprime positive arithmetic progression is never a perfect square: the case $(k,\ell)=(5,2)$, answered in the negative.

1975_06_01_erdos_selfridge: Erdős and Selfridge's refereed theorem (Illinois J. Math. 1975) that no product of two or more consecutive positive integers is a perfect power, which settles the case $d=1$ of the question in the negative.

1985_09_01_marszalek: Marszałek's refereed theorem (Monatsh. Math. 1985) that for a fixed common difference $d$ the product of $k$ terms is never a perfect power once $k$ exceeds an explicit bound in $d$.

2004_09_01_gyory_hajdu_saradha: The refereed theorem of Győry, Hajdu and Saradha (Canad. Math. Bull. 2004) that a product of four or five consecutive terms of a coprime positive arithmetic progression is never a perfect power.

2006_03_01_bennett_bruin_gyory_hajdu: The refereed theorem of Bennett, Bruin, Győry and Hajdu (Proc. London Math. Soc. 2006) that a product of $k$ consecutive terms of a coprime positive arithmetic progression is never a perfect power for $4\le k\le11$.

2009_07_01_gyory_hajdu_pinter: The refereed theorem of Győry, Hajdu and Pintér (Compos. Math. 2009) that a product of $k$ consecutive terms of a coprime positive arithmetic progression is never a perfect power for $3<k<35$.

2017_09_04_bennett_siksek: Bennett and Siksek's refereed theorem (Ann. of Math. 2020) that for every length $k\ge k_0$ no coprime positive progression of $k$ terms has a product equal to an $\ell$th power with $\ell$ prime and $\ell>\exp(10^k)$.

2026_09_10_piscitelli: D. Michael Piscitelli's Lean development, made with Claude Code, proving that the product of four terms of a coprime positive arithmetic progression is never a square, the case $(k,\ell)=(4,2)$; not built by this corpus.

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