PRIMES IN A PRESCRIBED ARITHMETIC PROGRESSION DIVIDING THE SEQUENCE $\{a^k+b^k\}_{k=1}^{\infty}$

DOI10.1142/S1793042109002316zbMath1190.11052arXivmath/0703925OpenAlexW1729285580MaRDI QIDQ3635801

Pieter Moree, Balasubramanian Sury

Publication date: 6 July 2009

Published in: International Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0703925

zbMATH Keywords

primes in progressionsapplications of the Chebotarev density theorem

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Distribution of integers in special residue classes (11N69)

Related Items (4)

On the distribution of balanced subgroups ⋮ Moser's mathemagical work on the equation \(1^k+2^k+\ldots+(m-1)^k=m^k\) ⋮ Prime divisors of \(\ell\)-Genocchi numbers and the ubiquity of Ramanujan-style congruences of level \(\ell\) ⋮ Multiplicative Order and Frobenius Symbol for the Reductions of Number Fields

Cites Work

• Unnamed Item
• A conjecture of Krishnamurthy on decimal periods and some allied problems
• On the distribution of the order and index of \(g \pmod p\) over residue classes. II
• On the distribution of the order and index of \(g\pmod p\) over residue classes. III.
• Über die Dichte der Primzahlen \(p\), für die eine vorgegebene ganzrationale Zahl \(a\neq 0\) von gerader bzw. ungerader Ordnung \(\mod p\) ist
• On the representations of \(-1\) as a sum of squares in a cyclotomic field
• Determination of the Stufe of certain cyclotomic fields
• On the representation of \(-1\) as a sum of two-squares in an algebraic number field
• On the distribution of the order and index of \(g\) (mod \(p\)) over residue classes. I
• The distribution of integers represented by binary quadratic forms

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