We give an upper bound on the number of extensions of a triple to a quadruple for the Diophantine m-tuples with the property D(4). We also confirm the conjecture of the uniqueness of such an extension in some special cases.

中文翻译：

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具有属性$$ D（4）$$ D（4）的Diophantine三元组的扩展

对于具有属性D（4）的Diophantine m-元组，我们给出了三重到四重的扩展数的上限。我们还确认了在某些特殊情况下这种扩展的唯一性的猜想。