On the products \((1^\ell +1)(2^\ell +1)\cdots (n^\ell +1)\)

DOI10.1016/j.jnt.2013.01.003zbMath1319.11004OpenAlexW1538330524MaRDI QIDQ2444991

Ming-Liang Gong, Xiao-Zhi Ren, Yong-Gao Chen

Publication date: 11 April 2014

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2013.01.003

zbMATH Keywords

productBertrand's postulateDirichlet's theorempowerful numbershifted power

Mathematics Subject Classification ID

Factorization; primality (11A51)

Related Items (7)

On the products \((1^{3}+q^{3})(2^{3}+q^{3})\cdots (n^{3}+q^{3})\) ⋮ On the Occurrence of Perfect Squares Among Values of Certain Polynomial Products ⋮ On the products \((1^\ell + 1)(2^\ell + 1)\cdots(n^\ell + 1)\). II ⋮ 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 ⋮ Prime powers dividing products of consecutive integer values of \(x^{2^n}+1\) ⋮ Polynomial products modulo primes and applications

Cites Work

• Unnamed Item
• Powerful numbers in \((1^k +1)(2^k+1) \cdots (n^k +1)\)
• Arithmetical properties of a sequence arising from an arctangent sum
• Squares in \((1^2+1)\dots(n^2+1)\)
• A note on the products \((1^\mu +1)(2^\mu +1)\dots (n^\mu +1)\)
• Handbook of Number Theory I
• Neither (4k 2 + 1) nor (2k(k – 1) + 1) is a Perfect Square

This page was built for publication: On the products \((1^\ell +1)(2^\ell +1)\cdots (n^\ell +1)\)