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if (h, k) 1. He remarked: "When s = 2 or s>8, this conclusion is false. The cases s =3 and s =4 are exceptional. The conclusion is true, but new difficulties arise in the proof because the series used are not all absolutely convergent. These difficulties are easily surmounted when s =4, but are more serious when s = 3." It is the purpose of this paper to show that in spite of these convergence

On the representations of a number as the sum of three squares