Lower bounds for the least common multiple of finite arithmetic progressions

DOI10.1016/j.crma.2006.11.002zbMath1156.11004OpenAlexW1989394048MaRDI QIDQ858917

Weiduan Feng, Shao-Fang Hong

Publication date: 11 January 2007

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2006.11.002

Mathematics Subject Classification ID

Arithmetic progressions (11B25) Multiplicative structure; Euclidean algorithm; greatest common divisors (11A05)

Related Items (19)

The least common multiple of consecutive terms in a cubic progression ⋮ Nontrivial effective lower bounds for the least common multiple of a $q$-arithmetic progression ⋮ Uniform lower bound for the least common multiple of a polynomial sequence ⋮ On the sum of reciprocals of least common multiples ⋮ On a conjecture of Fox-Kleitman and additive combinatorics ⋮ Note on the lower bound of least common multiple ⋮ New lower bounds for the least common multiples of arithmetic progressions ⋮ Improvements of lower bounds for the least common multiple of finite arithmetic progressions ⋮ On the periodicity of an arithmetical function ⋮ Further improvements of lower bounds for the least common multiples of arithmetic progressions ⋮ The least common multiple of consecutive arithmetic progression terms ⋮ On the sum of reciprocals of least common multiples. II ⋮ New lower bounds for the least common multiple of polynomial sequences ⋮ Nontrivial upper bounds for the least common multiple of an arithmetic progression ⋮ Nontrivial effective lower bounds for the least common multiple of some quadratic sequences ⋮ New results on the least common multiple of consecutive integers ⋮ The exact upper bound for the sum of reciprocals of least common multiples ⋮ The sum of reciprocals of least common multiples ⋮ A characterization of finite arithmetic progressions via regular partitions of quadrilaterals

Cites Work

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• The primes contain arbitrarily long arithmetic progressions
• Nontrivial lower bounds for the least common multiple of some sequences of integers.
• On Chebyshev-Type Inequalities for Primes
• ASYMPTOTIC BEHAVIOR OF EIGENVALUES OF GREATEST COMMON DIVISOR MATRICES
• On the Product of the Primes

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