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On variants of the abc conjecture in terms of Lehmer means

In this post we denote the Lehmer mean of a tuple $\text{x}$ of positive real numbers as $$L_p(\text{x})={\sum_{k=1}^nx_k^p\over\sum_{k=1}^nx_k^{p-1}},$$ see the reference Wikipedia Lehmer mean. The ...
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