The Generalized Nagell–Ljunggren Problem: Powers with Repetitive Representations

DOI10.1080/10586458.2017.1419391zbMath1475.11050arXiv1707.03894OpenAlexW2963387177MaRDI QIDQ4972537

Robert J. Lemke Oliver, Arlo Shallit, Andrew Bridy, Jeffrey O. Shallit

Publication date: 25 November 2019

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1707.03894

zbMATH Keywords

power\(abc\)-conjecturerepetitionDiophantine equationbase-\(b\) representationNagell-Ljunggren problem

Mathematics Subject Classification ID

Computer solution of Diophantine equations (11Y50) Radix representation; digital problems (11A63) Exponential Diophantine equations (11D61) Higher degree equations; Fermat's equation (11D41)

Related Items (1)

Unnamed Item

Uses Software

• OEIS

Cites Work

• New bounds and conditions for the equation of Nagell-Ljunggren
• Solving the Pell equation
• A weak effective \(abc\)-conjecture
• On the Oesterlé-Masser conjecture
• The Nagell-Ljunggren equation \(\frac{x^n-1}{x-1}=y^q\)
• On the Diophantine equation \({x^ n-1\over x-1}=y^ q\).
• The \(abc\) conjecture
• The Nagell-Ljunggren equation via Runge's method
• Rational approximation to algebraic numbers of small height: the Diophantine equation |axn - byn|= 1
• Zeroless Positional Number Representation and String Ordering
• Sur L'équation Diophantienne (x ⁿ −1)/(x −1)=y ^q , III
• An Explicit Bound for Aliquot Cycles of Repdigits
• A refinement of theabcconjecture
• Class Number Conditions for the Diagonal Case of the Equation of Nagell and Ljunggren
• On the Nagell-Ljunggren equation $(x^n - 1)/(x - 1) = y^q$
• The Mystique of Repunits
• Sur l'équation diophantienne
• A note on the diophantine equation (x^m − l) / (x − 1) = yⁿ + l
• Baker's explicit abc-conjecture and applications
• On integers with identical digits
• The equation formula here has no solution with x square
• Rational and Integral Points on Quadratic Twists of a Given Hyperelliptic Curve
• Monadic Elementary Formal Systems
• Einige Bemerkungen über die Darstellung ganzer Zahlen durch binäre kubische Formen mit positiver Diskriminante
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: The Generalized Nagell–Ljunggren Problem: Powers with Repetitive Representations