Abstract

Prof. Landau has called my attention to H. W. Richmond's paper, “An elementary note upon Waring's problem for cubes, positive and negative”, Messenger of Math., 51 (1922), 177–186. Richmond has anticipated me and my correspondents in the formulae of decomposition (3), (8), (9), (11), (13), (14), (15), (16), (17) in § 1, including in particular the formulae giving the decompositions into four integer cubes of 6k+3, 18k+1. 18k+8. The result in § 3, that corresponding formulae for 9k+4 are impossible, has also been given by him.

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