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In relation to Hall's conjecture , a new algorithm is presented to search for small nonzero k = |x 3 − y 2 | values. Thirteen new values of k < x 1/2 are reported. Dealing with natural numbers, the difference (1.1) k = x 3 − y 2 is zero when x = t 2 and y = t 3 but, in other cases, it seems difficult to achieve small absolute values. For a given k = 0,… (More)

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