Distribution of parity of the partition function in arithmetic progressions
نویسندگان
چکیده
منابع مشابه
Parity of the Partition Function in Arithmetic Progressions, Ii
Let p(n) denote the ordinary partition function. Subbarao conjectured that in every arithmetic progression r (mod t) there are infinitely many integers N ≡ r (mod t) for which p(N) is even, and infinitely many integers M ≡ r (mod t) for which p(M) is odd. We prove the conjecture for every arithmetic progression whose modulus is a power of 2.
متن کاملParity of the Partition Function in Arithmetic Progressions
Let p(n) denote the number of partitions of a non-negative integer n. A well-known conjecture asserts that every arithmetic progression contains infinitely many integers M for which p(M) is odd, as well as infinitely many integers N for which p(N) is even (see Subbarao [23]). In this paper we prove that there indeed are infinitely many integers N in every arithmetic progression for which p(N) i...
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15 صفحه اولParity of the Partition Function
Let p(n) denote the number of partitions of a non-negative integer n. A well-known conjecture asserts that every arithmetic progression contains infinitely many integers M for which p(M) is odd, as well as infinitely many integers N for which p(N) is even (see Subbarao [22]). From the works of various authors, this conjecture has been verified for every arithmetic progression with modulus t whe...
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ژورنال
عنوان ژورنال: Indagationes Mathematicae
سال: 1999
ISSN: 0019-3577
DOI: 10.1016/s0019-3577(99)80014-7