We consider the partition function b'p(n), which counts the number of partitions of the integer n into distinct parts with no part divisible by the prime p. We prove the following: Let p be a prime greater than 3 and let r be an integer between 1 and p - 1, inclusively, such that 24r + 1 is a quadratic nonresidue modulo p. Then, for all nonnegative integers n, b'p(pn + r) ≡ 0 (mod 2).
|Original language||English (US)|
|Number of pages||4|
|State||Published - Oct 1 2003|
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