We consider Diophantine equations of the shape \( f(x) = g(y) \), 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.

中文翻译：

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分离变量和多项式幂和中的丢番图方程

我们考虑形状为\( f(x) = g(y) \) 的丢番图方程，其中多项式f和g是幂和的元素。使用 Bilu 和 Tichy 的有限性标准，我们将证明在适当的假设下，无限多个具有有界分母的有理解 ( x ,  y ) 仅在微不足道的情况下才有可能。