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On gaps between numbers that are sums of three cubes
Published online by Cambridge University Press: 26 February 2010
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Let (Sn)n = 1,2,… be the strictly increasing sequence of those natural numbers that can be represented as the sum of three cubes of positive integers. The estimate
is easily proved as follows: Let x1 be the largest natural number with Then This procedure is iterated by choosing x2 and then x3 as the largest natural numbers satisfying and Thus Since this implies (1).
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