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Showing 1 to 4 of 4 for “"covering systems"”.
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Covering Systems
… one of the congruences, is said to be a set of covering congruences, or covering system. A famous conjecture of Erdos from 1950 states that the least modulus of a covering system can be arbitrarily large. This conjecture remains open, and, in its full strength, appears at present to be …
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Covering Systems of Polynomial Rings Over Finite Fields
… congruences with distinct moduli. He called such systems of congruences covering systems. Utilizing his covering system, he disproved a conjecture of de Polignac asking, “for every odd k, is there a prime of the form 2n + k?” Examples of covering systems of the integers are presented along with …
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Bijective proofs of partition identities and covering systems
… is discussed in Chapters 2 − 5. The second is on covering systems, which are considered in Chapters 6 − 8. In 2000, Farkas and Kra used their theory of theta functions to establish a beautiful theorem on colored partitions, and they asked for a bijective proof of it. In Chapter 2, we give a …
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Combinatorial Problems with Geometric Flavour
… \leq 3$. In Chapters 4, 5 and 6, we investigate covering systems. A covering system is a finite collection of arithmetic progressions $\{a_1\text{ }(\text{mod } m_1),a_2\text{ }(\text{mod } m_2), \hdots, a_k\text{ }(\text{mod } m_k) \}$ that cover the integers, i.e., $\cup_i \{a_i+ n m_i \text{ : …