Partitions with congruence conditions
نویسندگان
چکیده
منابع مشابه
Partitions with Early Conditions
In an earlier paper, partitions in which the smaller parts were required to appear at least k-times were considered. Some of those results were tied up with Rogers-Ramanujan type identities and mock theta functions. By considering more general conditions on initial parts we are led to natural explanations of many more identities contained in Slater’s compendium of 130 Rogers-Ramanujan identities.
متن کاملPartitions with difference conditions and Alder's conjecture.
In 1956, Alder conjectured that the number of partitions of n into parts differing by at least d is greater than or equal to that of partitions of n into parts identical with +/-1 (mod d+3) for d > or = 4. In 1971, Andrews proved that the conjecture holds for d = 2r-1, r > or = 4. We sketch a proof of the conjecture for all d > or = 32.
متن کاملNew Solvability Conditions for Congruence
K. Bibak et al. [arXiv:1503.01806v1 [math.NT], March 5 2015] proved that congruence ax ≡ b (mod n) has a solution x0 with t = gcd(x0, n) if and only if gcd ( a, n t ) = gcd ( b t , n t ) thereby generalizing the result for t = 1 proved by B. Alomair et al. [J. Math. Cryptol. 4 (2010), 121–148] and O. Grošek et al. [ibid. 7 (2013), 217–224]. We show that this generalized result for arbitrary t f...
متن کاملOn Congruence Conditions for Primality
For any k ≥ 0, all primes n satisfy the congruence nσk(n) ≡ 2 mod φ(n). We show that this congruence in fact characterizes the primes, in the sense that it is satisfied by only finitely many composite n. This characterization generalizes the results of Lescot and Subbarao for the cases k = 0 and k = 1. For 0 ≤ k ≤ 14, we enumerate the composite n satisfying the congruence. We also prove that an...
متن کاملOn the asymmetric divisor problem with congruence conditions
A certain generalized divisor function d(n) is studied which counts the number of factorizations of a natural number n into integer powers with prescribed exponents under certain congruence restrictions. An Ω-estimate is established for the remainder term in the asymptotic for its Dirichlet summatory function.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1976
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1976-0404184-7