Journal of Integer Sequences, Vol. 20 (2017), Article 17.2.7

On the Exponents of Non-Trivial Divisors of Odd Numbers and a Generalization of Proth's Primality Theorem

Tom Müller
Institut für Cusanus-Forschung
University and Theological Faculty of Trier
Domfreihof 3
54290 Trier


We present a family of integer sequences characterizing the behavior of the quotients σ/s for a given odd natural number H, where N = H · 2σ + 1 is a composite number and h · 2s + 1 (h ≥ 1 odd, s, σ ∈ N) is a non-trivial divisor of N. As an application we prove a generalization of the primality theorem of Proth.

Full version:  pdf,    dvi,    ps,    latex    

(Concerned with sequences A000125 A102742 A128852 A272894 A272895.)

Received May 12 2016; revised version received December 1 2016. Published in Journal of Integer Sequences, December 27 2016.

Return to Journal of Integer Sequences home page