On the products \((1^{3}+q^{3})(2^{3}+q^{3})\cdots (n^{3}+q^{3})\)

DOI10.1016/j.jnt.2017.04.012zbMath1384.11059OpenAlexW2622922651MaRDI QIDQ2401202

Chuan Ze Niu, Wenxin Liu

Publication date: 31 August 2017

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

Full work available at URL: https://doi.org/10.1016/j.jnt.2017.04.012

zbMATH Keywords

powerful numbers\(p\)-adic valuations

Mathematics Subject Classification ID

Cubic and quartic Diophantine equations (11D25)

Related Items (2)

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

Cites Work

• Unnamed Item
• On the products \((1^\ell + 1)(2^\ell + 1)\cdots(n^\ell + 1)\). II
• Powerful numbers in \((1^k +1)(2^k+1) \cdots (n^k +1)\)
• Diophantine equations with products of consecutive values of a quadratic polynomial
• On squares in polynomial products
• Arithmetical properties of a sequence arising from an arctangent sum
• Squares in \((1^2+1)\dots(n^2+1)\)
• A note on the products \((1^\mu +1)(2^\mu +1)\dots (n^\mu +1)\)
• Powers in \(\prod_{k=1}^n (ak^{2^l\cdot3^m}+b)\)
• On the products \((1^\ell +1)(2^\ell +1)\cdots (n^\ell +1)\)
• SQUARES IN (2² - 1)…(n² - 1) AND p-ADIC VALUATION
• The 𝑘^{𝑡ℎ} prime is greater than 𝑘(ln𝑘+lnln𝑘-1) for 𝑘≥2

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