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引用次数: 0
摘要
我们考虑 f ( x ) = g ( y ) 形状的二叉方程，其中多项式 f 和 g 是幂和的元素。我们将利用比鲁和蒂奇的有限性准则证明，在适当的假设条件下，分母有界的无穷多个有理解 (x, y) 只可能在微不足道的情况下出现。
Diophantine equations in separated variables and polynomial power sums.
We consider Diophantine equations of the shape , where the polynomials f and g are elements of power sums. Using a finiteness criterion of Bilu and Tichy, we will prove that under suitable assumptions infinitely many rational solutions (x, y) with a bounded denominator are only possible in trivial cases.
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