5 papers
The 3x+1 and 5x+1 Problems
Robert Tremblay
We will prove that there are trajectories generated by the function at the origin of the 5x+1 problem which are divergent. The iterative application of this function on the set of…
Distribution function
Robert Tremblay
From a known result of diophantine equations of the first degree with 2 unknowns we simply find the results of the distribution function of the sequences of positive integers gener…
Generalized 3x+1 Mappings : convergence and divergence
Robert Tremblay
Discussion about the convergence and divergence of trajectories generated by certain functions derived from generalized 3x+1 mappings
Generalized 3x + 1 Mappings : counting cycles
Robert Tremblay
We demonstrate that the number of cycles for two problems of the family of generalized 3x+1 mappings is possible finite.
Generalized 3x + 1 Mappings : searching for cycles
Robert Tremblay
We determine the conditions for the existence or not of cycles for several families of generalized 3x + 1 mappings and develop a method to find them.