Parity Results for p-Regular Partitions with Distinct Parts
نویسنده
چکیده
We consider the partition function bp(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, bp(pn + r) ≡ 0 (mod 2).
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ورودعنوان ژورنال:
- Ars Comb.
دوره 69 شماره
صفحات -
تاریخ انتشار 2003