On integers of the form 𝑘2ⁿ+1

DOI10.1090/S0002-9939-00-05916-5zbMath1010.11004MaRDI QIDQ4517471

Yong-Gao Chen

Publication date: 22 November 2000

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

covering systemlinear forms in \(p\)-adic logarithmsprimitive prime factor

Mathematics Subject Classification ID

Congruences; primitive roots; residue systems (11A07) Arithmetic progressions (11B25)

Related Items (13)

ON SHIFTED PRIMES AND BALANCED PRIMES ⋮ On integers of the forms \(k\pm 2^{n}\) and \(k2^{n}\pm 1\) ⋮ Nonlinear Sierpiński and Riesel numbers ⋮ On Romanoff's constant ⋮ On the integers of the form $p^{2}+b^{2}+2^{n}$ and $b_{1}^{2}+b_{2}^{2}+2^{n^{2}}$ ⋮ Five consecutive positive odd numbers, none of which can be expressed as a sum of two prime powers ⋮ Five consecutive positive odd numbers none of which can be expressed as a sum of two prime powers. II ⋮ FLAT PRIMES AND THIN PRIMES ⋮ On the density of integers of the form \(2^k + p\) in arithmetic progressions ⋮ ON THE DENSITY OF INTEGERS OF THE FORM (p−1)2⁻ⁿ IN ARITHMETIC PROGRESSIONS ⋮ Unnamed Item ⋮ On integers of the forms \(k-2^n\) and \(k2^n+1\) ⋮ On integers of the forms \(k^r-2^n\) and \(k^r2^n+1\).

Cites Work

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• On the density of odd integers of the form \((p-1)2^{-n}\) and related questions
• Explicit Primality Criteria for h ⋅2 k ± 1
• New Primes of the Form k ⋅2 n + 1
• A Report on Primes of the Form k⋅2 n + 1 and On Factors of Fermat Numbers
• The Problem of Sierpinski Concerning k ⋅2 n + 1
• On the Smallest k Such that All k ⋅2 N + 1 are Composite
• On integers of the form $2^k\pm p^{\alpha _1}_1p^{\alpha _2}_2\dotsb p^{\alpha _r}_r$
• On the fractional parts of the powers of a rational number (II)
• Covering the Set of Integers by Congruence Classes of Distinct Moduli
• Rational approximations to algebraic numbers

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