Polynomial values of sums of products of consecutive integers

DOI10.1007/s00605-017-1130-2zbMath1442.11055OpenAlexW2766975353MaRDI QIDQ1673734

Attila Bérczes, András Bazsó, Florian Luca, Lajos Hajdu

Publication date: 14 September 2018

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: http://real.mtak.hu/91273/1/BBHL-SumsOfProducts.pdf

zbMATH Keywords

sums of productsblocks of consecutive integerspolynomial values

Mathematics Subject Classification ID

Higher degree equations; Fermat's equation (11D41)

Related Items (8)

Polynomial values of sums of hyperbolic binomial coefficients ⋮ Power values of sums of certain products of consecutive integers and related results ⋮ Polynomial values of figurate numbers ⋮ On linear combinations of products of consecutive integers ⋮ Diophantine equations connected to the Komornik polynomials ⋮ Polynomial values of products of terms from an arithmetic progression ⋮ On special extrema of polynomials with applications to Diophantine problems ⋮ Diophantine equations in separated variables and polynomial power sums

Cites Work

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• On \(S\)-integral solutions of the equation \(y^ m=f(x)\)
• The product of consecutive integers is never a power
• On the Diophantine equation \(x(x + 1)(x + 2)\dots (x + (m - 1)) =g(y)\)
• Power values of sums of products of consecutive integers
• INDECOMPOSABILITY OF POLYNOMIALS AND RELATED DIOPHANTINE EQUATIONS
• On the equation $y^m = P(x)$
• The Diophantine equation f(x) = g(y)
• Equal values of standard counting polynomials

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