TY - JOUR

T1 - On strong pseudoprimes in arithmetic progressions

AU - Van Der Poorten, A. J.

AU - Rotkiewicz, A.

PY - 1980

Y1 - 1980

N2 - 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 C2’≡ 1 (modN) 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.

AB - 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 C2’≡ 1 (modN) 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.

UR - http://www.scopus.com/inward/record.url?scp=84971697821&partnerID=8YFLogxK

U2 - 10.1017/S1446788700021315

DO - 10.1017/S1446788700021315

M3 - Article

AN - SCOPUS:84971697821

SN - 1446-7887

VL - 29

SP - 316

EP - 321

JO - Journal of the Australian Mathematical Society

JF - Journal of the Australian Mathematical Society

IS - 3

ER -