Solutions to the Equations 2w – 3n ± 1=0 with w and n Positive Integers
Alain Jaeckel *
Ecole Européenne de Strasbourg, 70, Boulevard d’Anvers, 67000 Strasbourg, France.
Jean-François Palierne
Ecole Normale Supérieur de Lyon, Laboratoire de Physique, 69364 Lyon, France.
Jean Dayantis
Institut Charles Sadron, Centre de Recherches Sur Les Macromolécules, 67034 Strasbourg, France (Retd.).
*Author to whom correspondence should be addressed.
Abstract
We show that the equations 2w – 3n ± 1 = 0, where w and n are positive integers, have no other solutions than (w,n) = (1,0), (1,1), (2,1) and (3,2)1.
Keywords: Number theory, Catalan conjecture, harmonical numbers, syracuse-collatz conjecture, unsolved arithmetic problems, Jeffrey C. Lagarias.