【摘要】 运用了一种初等的证明方法,对一个不定方程x(x+1)(x+2)(x+3)=11y(y+1)(y+2)(y+3)的正整数解进行了研究。证明过程中仅涉及到了初等的数论知识,就是采用了递归序列的方法,证明了不定方程x(x+1)(x+2)(x+3)=11y(y+1)(y+2)(y+3)无正整数解,同时这个证明过程也给出了这个不定方程组的全部整数解,它们是(x,y)=(-3,0),(-3,-1),(-3,-2),(-3,-3),(-2,0),(-2,-1),(-2,-2),(-2,-3),(-1,0),(-1,-1),(-1,-2),(-1,-3),(0,0),(0,-1),(0,-2),(0,-3)。更多还原

【Abstract】 In this paper using the method of recurrence sequences we show that there does not exist positive solution in the equation of the title.In fact,we obtain a more general result that the only integer solutions of the Diophantine equation is as follows: x(x+1)(x+2)(x+3)=11y(y+1)(y+2)(y+3)are(x,y)=(-3,0),(-3,-1),(-3,-2),(-3,-3),(-2,0),(-2,-1),(-2,-2),(-2,-3),(-1,0),(-1,-1),(-1,-2),(-1,-3),(0,0),(0,-1),(0,-2),(0,-3).更多还原