Generalized balancing numbers

DOI10.1016/S0019-3577(09)80005-0zbMath1239.11035OpenAlexW1986913327MaRDI QIDQ1042756

Florian Luca, Kálmán Liptai, Ákos Pintér, László Szalay

Publication date: 7 December 2009

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

Full work available at URL: https://doi.org/10.1016/s0019-3577(09)80005-0

zbMATH Keywords

exponential Diophantine equations

Mathematics Subject Classification ID

Exponential Diophantine equations (11D61)

Related Items (17)

Unnamed Item ⋮ On the Properties of Balancing and Lucas-Balancing $p$-Numbers ⋮ Balancing with binomial coefficients ⋮ Unnamed Item ⋮ Periodicity of balancing numbers ⋮ Two generalizations of dual-complex Lucas-balancing numbers ⋮ Unnamed Item ⋮ The Tribonacci-type balancing numbers and their applications ⋮ Unnamed Item ⋮ The Diophantine equation \(8x^2-y^2+8x(1+t)+(2t+1)^2=0\) and \(t\)-balancing numbers ⋮ Balancing polynomials and their derivatives ⋮ On the properties of k-balancing and k-Lucas-balancing numbers ⋮ Classes of gap balancing numbers ⋮ A Hasse-type principle for exponential Diophantine equations over number fields and its applications ⋮ Unnamed Item ⋮ Polynomial values of surface point counting polynomials ⋮ \(k\)-gap balancing numbers

Cites Work

• On \(S\)-integral solutions of the equation \(y^ m=f(x)\)
• On the Diophantine equation \(1^k+2^k+\dots +x^k+R(x)=y^2\)
• The Diophantine equation f(x) = g(y)
• On equal values of power sums
• Integral Points on Certain Elliptic Curves
• The House Problem
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