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...