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On the pseudoprimes of the form ax + b

Published online by Cambridge University Press:  24 October 2008

A. Rotkiewicz
A. Rotkiewicz
Affiliation:
Department of Pure Mathematics, University of Cambridge
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Extract

A composite number n is called a pseudoprime if n|2n− 2.

Theorem 1. If a and b are natural numbers such that (a, b) = 1, then there exist infinitely many pseudoprimes of the form ax + b, where x is a natural number.

The proof of this theorem is given by the author in (5). This proof is based on the following two lemmas.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 2 , April 1967 , pp. 389 - 392
Copyright
Copyright © Cambridge Philosophical Society 1967

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References

REFERENCES

(1)Bang, A. S.Thaltheoretiske Undersogelser. Tidsskrift for Math. (5), 4 (1886), 70–80, 130–137Google Scholar
(2)Birkhoff, G. D. and Vandiver, H. S.On the integral divisors of an − bn. Ann. of Math. (2), 5 (1904), 173–180.CrossRefGoogle Scholar
(3)Kanold, H. J.Sätze über Kristeilungspolynome und ihre Anwendungen and einige zahlentheoretische Probleme. J. für Math. 187 (1950), 169–172.Google Scholar
(4)Prachar, K.Primzahlverteilung (Berlin–Gottingen–Heidelberg, 1957).Google Scholar
(5)Rotkiewicz, A.Sur les nombres pseudoprimes de la forme ax + b, C.R. Acad. Sci. Paris 257 (1963), 2601–2607.Google Scholar
(6)Schinzel, A.On primitive prime factors of an − bn, Proc. Cambridge Philos. Soc. 58 (1962), 555–562.Google Scholar
(7)Zsigmondy, K.Zur Theorie der Potenzreste Monatsh. Math. 3 (1892), 265–284.CrossRefGoogle Scholar