Primes in Arithmetic Progressions

J. J. P. Veerman ()
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J. J. P. Veerman: Portland State University

Chapter Chapter 14 in Numbers from all Angles, 2026, pp 293-319 from Springer

Abstract: Abstract An arithmetic progression Arithmetic progressionis a set S of integers of the form $$\underline{S(a,q)}$$S(a,q)̲ S(a, q), where $$\begin{aligned} S(a,q):=\{a+kq\,:\, q\in \mathbb {N}, k\in \mathbb {Z}\} . \end{aligned}$$S(a,q):={a+kq:q∈N,k∈Z}.In this chapter we will only consider sets of the form $$S(a,q)\cap \mathbb {N}$$S(a,q)∩N. For brevity, however, we will simply continue to write S(a, q). If $$\gcd (a,q)=d>1$$gcd(a,q)=d>1, then any two distinct numbers in S have a common divisor greater than 1.

Date: 2026
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DOI: 10.1007/978-3-032-10000-9_14

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