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On strong pseudoprimes in arithmetic progressions

Published online by Cambridge University Press:  09 April 2009

A. J. van der Poorten  and
A. Rotkiewicz
A. J. van der Poorten
Affiliation:
School of Mathematics and Physics Macquarie UniversityNorth Ryde, N.S.W. 2113, Australia
A. Rotkiewicz
Affiliation:
Instytut Matematyczmy PAN ul.Sniadeckich 8 00-950 Warszawa, Poland
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Abstract

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A composite integer N is said to be a strong pseudoprime for the base C if with N – 1 = 2sd, (2, d) = 1 either Cd = 1, or C2r ≡ 1 (mod N) some r, 0 ≤ r < s. It is shown that every arithmetic progression ax+b (x = 0,1, …) where a, b are relatively prime integers contains an infinite number of odd strong pseudoprimes for each base C ≤ 2.

1980 Mathematics subject classification (Amer. Math. Soc.): 10 A 15.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 29 , Issue 3 , May 1980 , pp. 316 - 321
Copyright
Copyright © Australian Mathematical Society 1980

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