ON THE DENSITY OF INTEGERS OF THE FORM (p−1)2−n IN ARITHMETIC PROGRESSIONS

DOI10.1017/S0004972708000804zbMath1218.11010OpenAlexW2088053710MaRDI QIDQ3603860

Jin-Hui Fang, Xue-Gong Sun

Publication date: 19 February 2009

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0004972708000804

zbMATH Keywords

asymptotic densityarithmetic progressionscovering systems

Mathematics Subject Classification ID

Goldbach-type theorems; other additive questions involving primes (11P32) Density, gaps, topology (11B05) Arithmetic progressions (11B25)

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On a problem of Romanoff type ⋮ Tight upper and lower bounds for the reciprocal sum of Proth primes

Cites Work

• On integers of the forms \(k\pm 2^{n}\) and \(k2^{n}\pm 1\)
• On the density of odd integers of the form \((p-1)2^{-n}\) and related questions
• On Romanoff's constant
• On integers of the forms \(k-2^n\) and \(k2^n+1\)
• On integers of the forms \(k^r-2^n\) and \(k^r2^n+1\).
• On integers of the form 𝑘2ⁿ+1
• Five consecutive positive odd numbers, none of which can be expressed as a sum of two prime powers
• Fibonacci numbers that are not sums of two prime powers
• On integers of the form $2^k\pm p^{\alpha _1}_1p^{\alpha _2}_2\dotsb p^{\alpha _r}_r$
• Unsolved problems in number theory

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