A note of the Conjectured of Sierpinski on triangular numbers
نویسنده
چکیده
Recently, Bennett arononled that he proved a conjecture of Sierpinski on triangular numbers. In this paper, we firstly modified the mistakes in reference [7] of Bennett and [8] of Chen and Fang, and then using Störmer’s theorem of the solutions of Pell equation, and a deep result of primitive divisor of Bilu, Hanrot and Voutier, we proved that there do not exist four distinct triangular numbers in geometric progression {AQ}r=1. Therefore we totally solved the question of Sierpinski on triangular numbers.
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