On the Occurrence of Perfect Squares Among Values of Certain Polynomial Products

DOI10.4169/amer.math.monthly.123.6.597zbMath1391.11015OpenAlexW2418698021WikidataQ58281217 ScholiaQ58281217MaRDI QIDQ4576137

Erhan Gürel

Publication date: 12 July 2018

Published in: The American Mathematical Monthly (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4169/amer.math.monthly.123.6.597

zbMATH Keywords

perfect squares

Mathematics Subject Classification ID

Counting solutions of Diophantine equations (11D45) Polynomials in number theory (11C08) Factorization; primality (11A51)

Related Items

Products of consecutive values of some quartic polynomials ⋮ Numbers of the form \((1^{\ell}+q^{\ell})(2^{\ell}+q^{\ell})\cdots(n^{\ell}+q^\ell)\) that are not powerful ⋮ An infinite collection of quartic polynomials whose products of consecutive values are not perfect squares

Cites Work

• Powerful numbers in \((1^k +1)(2^k+1) \cdots (n^k +1)\)
• Squares in \((1^2+1)\dots(n^2+1)\)
• A note on the products \((1^\mu +1)(2^\mu +1)\dots (n^\mu +1)\)
• On the products \((1^\ell +1)(2^\ell +1)\cdots (n^\ell +1)\)
• Neither (4k 2 + 1) nor (2k(k – 1) + 1) is a Perfect Square