On the Representations of Integers by the Sextenary
نویسنده
چکیده
Abstract. In this paper we derive an explicit formula for the number of representations of an integer by the sextenary form x + y + z + 7s + 7t + 7u. We establish the following intriguing inequalities 2b(n) ≥ a7(n) ≥ b(n) for n 6= 0, 2, 6, 16. Here a7(n) is the number of partitions of n that are 7-cores and b(n) is the number of representations of n +2 by the sextenary form (x + y + z + 7s + 7t + 7u)/8 with x, y, z, s, t and u being odd.
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