共查询到20条相似文献,搜索用时 15 毫秒
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Yuchen Ding 《Comptes Rendus Mathematique》2019,357(6):483-486
Assuming the abc conjecture, Silverman proved that, for any given positive integer , there are primes such that . In this paper, we show that, for any given integers and , there still are primes satisfying and , under the assumption of the abc conjecture. This improves a recent result of Chen and Ding. 相似文献
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Let be a prime. In this paper, with the help of Jacobsthal sums over finite fields, we study some permutation problems involving biquadratic residues modulo p. 相似文献
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《Discrete Mathematics》2022,345(2):112663
Given graphs F and H, the generalized rainbow Turán number is the maximum number of copies of F in an n-vertex graph with a proper edge-coloring that contains no rainbow copy of H. B. Janzer determined the order of magnitude of for all and , and a recent result of O. Janzer implied that . We prove the corresponding upper bound for the remaining cases, showing that . This matches the known lower bound for k even and is conjectured to be tight for k odd. 相似文献
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《Discrete Mathematics》2021,344(12):112596
A holey Mendelsohn triple system (HMTS) is a decomposition of a complete multipartite directed graph into directed cycles of length 3. If the directed cycles of length 3 can be partitioned into parallel classes, then the HMTS is called an RHMTS. Bennett, Wei and Zhu [J. Combin. Des., 1997] showed that an RHMTS of type exists when and with some possible exceptions. In this paper, motivated by the application in constructing RHMTSs, we investigate the constructions of holey Mendelsohn frames. We prove that a 3-MHF of type exists if and only if , and , and then determine that the necessary condition for the existence of an RHMTS of type , namely, is also sufficient except for . New recursive constructions on incomplete RHMTSs via MHFs are introduced to settle this problem completely. 相似文献
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