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Quadruples in the Four-Number Game with Large Termination Times


IJMEST Volume 33, Number 6, ISSN 0020-739X


The discrete dynamical system of absolute differences defined by the map [psi]( x[subscript 1] , x[subscript 2] , x[subscript 3] , x[subscript 4] ) = ([vertical line] x[subscript 2] - x[subscript 1] [vertical line], [vertical line] x[subscript 3] - x[subscript 2] [vertical line], [vertical line] x[subscript 4] - x[subscript 3] [vertical line], [vertical line] x[subscript 1] - x[subscript 4] [vertical line]) has been studied by many authors and one of the interesting questions is how to locate quadruples which converge to the fixed point (0, 0, 0, 0) in large numbers of steps. An elementary method is offered for obtaining such quadruples. The method is also able to find quadruples that will not converge to (0, 0, 0, 0). (Contains 2 tables.)


Yueh, W.C. & Cheng, S.S. (2002). Quadruples in the Four-Number Game with Large Termination Times. International Journal of Mathematical Education in Science and Technology, 33(6), 879-891. Retrieved September 19, 2019 from .

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