We address the Uniform Boundedness Conjecture of Morton and Silverman in the case of unicritical polynomials, assuming a generalization of the abc-conjecture. For unicritical polynomials of degree at least five, we require only the standard abc-conjecture.

中文翻译：

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动态一致有界性和abc-猜想

我们解决莫顿西尔弗曼的一致有界性猜想在unicritical多项式的情况下，假设的推广ABC -conjecture。至少五度的unicritical多项式，我们只需要标准的ABC -conjecture。