On the theorem of Wójcik
Glasgow mathematical journal, Tome 38 (1996) no. 2, pp. 157-162

Voir la notice de l'article provenant de la source Cambridge University Press

In the paper [3] the following lemma was proved.Lemma. Let a, b and c be positive integers such that a and be are relatively prime. Then there are infinitely many primes p in the arithmetic progression ax + b (x = 0,1,2,...) such that
Rotkiewicz, A. On the theorem of Wójcik. Glasgow mathematical journal, Tome 38 (1996) no. 2, pp. 157-162. doi: 10.1017/S0017089500031384
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[1] 1.Durst, L. K., Exceptional real Lehmer sequences, Pacific J. Math. 9 (1959), 437–441. Google Scholar | DOI

[2] 2.Lehmer, D. H., An extended theory of Lucas functions, Ann. Math. (2) 31 (1930), 419–448. Google Scholar | DOI

[3] 3.Rotkiewicz, A., On the prime factors of the number 2P−1–1, Glasgow Math. J. 9 (1968), 83–86. Google Scholar | DOI

[4] 4.Rotkiewicz, A., On the pseudoprimes of the form ax + b with respect to the sequence of Lehmer, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 20 (1972), 349–354. Google Scholar

[5] 5.Rotkiewicz, A., On Euler Lehmer pseudoprimes and strong Lehmer pseudoprimes with parameters L, Q in arithmetic progressions, Math. Comp. 39 (1982), 239–247. Google Scholar

[6] 6.Rotkiewicz, A., On strong Lehmer pseudoprimes in the case of negative discriminant in arithmetic progression, Ada Arith. 68 (1994), 145–151. Google Scholar | DOI

[7] 7.Schinzel, A., The intrinsic divisors of Lehmer numbers in the case of negative discriminant, Ark. Math. 4 (1962), 413–416. Google Scholar | DOI

[8] 8.Stewart, C. L., Primitive divisors of Lucas and Lehmer numbers, Transcendence Theory: Advances and Application (Academic Press, 1977), 79–92. Google Scholar

[9] 9.Ward, M., The intrinsic divisors of Lehmer numbers, Ann. Math..(2) 62 (1955), 230–236. Google Scholar | DOI

[10] 10.Wójcik, J., Contribution to the theory of Kummer extension, Ada Arith. 40 (1982), 155–174. Google Scholar | DOI

[11] 11.Wójcik, J., On the density of some sets of primes connected with cyclotomic polynomials, Ada Arith. 41 (1982), 117–131. Google Scholar | DOI

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