On the Diophantine equation \(x(x + 1)(x + 2)\dots (x + (m - 1)) =g(y)\)

DOI10.1016/S0019-3577(03)90069-3zbMath1096.11015MaRDI QIDQ1433180

Balasubramanian Sury, Manisha V. Kulkarni

Publication date: 15 June 2004

Published in: Indagationes Mathematicae. New Series (Search for Journal in Brave)

Mathematics Subject Classification ID

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

Related Items (15)

Polynomial values of sums of hyperbolic binomial coefficients ⋮ The Prouhet-Tarry-Escott problem, indecomposability of polynomials and Diophantine equations ⋮ Balancing with binomial coefficients ⋮ Polynomial values of sums of products of consecutive integers ⋮ Polynomial values of figurate numbers ⋮ The Diophantine equation f(x)=g(y)$f(x)=g(y)$ for polynomials with simple rational roots ⋮ Complete decomposition of Dickson-type polynomials and related Diophantine equations ⋮ Polynomial values of products of terms from an arithmetic progression ⋮ A class of Diophantine equations involving Bernoulli polynomials ⋮ Über den Zusammenhang zwischen der Eindeutigkeit und Lösbarkeit partieller Differentialgleichungen zweiter Ordnung vom elliptischen Typus . ⋮ On special extrema of polynomials with applications to Diophantine problems ⋮ Über den Zusammenhang zwischen der Eindeutigkeit und Lösbarkeit partieller Differentialgleichungen zweiter Ordnung vom elliptischen Typus ⋮ Extrema of polynomials with real roots and Diophantine equations ⋮ On the Diophantine equation \(F(\binom{x}{n})=b\binom{y}{m}\) ⋮ Polynomial values of surface point counting polynomials

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• Quadratic factors of f(x) -g(y)
• The Diophantine equation x(x+1)...(x+(m-1)) + r= yⁿ
• On the equation x(x+1)... (x+k-1) = y(y+d)... (y+(mk-1)d), m=1,2
• On arithmetic progressions of equal lengths with equal products

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