A simple (inductive) proof for the non-existence of 2-cycles of the \(3x+1\) problem

DOI10.1016/j.jnt.2006.05.011zbMath1111.11016OpenAlexW2162335506MaRDI QIDQ868892

John L. Simons

Publication date: 26 February 2007

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

Full work available at URL: https://doi.org/10.1016/j.jnt.2006.05.011

zbMATH Keywords

linear forms in logarithms\(3x+1\) problem

Mathematics Subject Classification ID

Special sequences and polynomials (11B83) Exponential Diophantine equations (11D61) Linear forms in logarithms; Baker's method (11J86)

Related Items (1)

On the nonexistence of nontrivial small cycles of the \(\mu\) function in \(3x+1\) conjecture

Cites Work

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• Linear forms in two logarithms and interpolation determinants
• Benford's law, values of L-functions and the 3x+1 problem
• The 3x + 1 Problem and Its Generalizations
• A lower bound for linear forms in logarithms
• On the "3x + 1" Problem
• On the nonexistence of $2$-cycles for the $3x+1$ problem
• Theoretical and computational bounds for m-cycles of the 3n+1-problem
• Counting smooth solutions to the equation A +B =C

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