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On Waring's problem: two squares, two cubes and two sixth powers (1212.6150v2)
Published 26 Dec 2012 in math.NT
Abstract: We investigate the number of representations of a large positive integer as the sum of two squares, two positive integral cubes, and two sixth powers, showing that the anticipated asymptotic formula fails for at most O((log X)3) positive integers not exceeding X.