A composite integer N is said to be a strong pseudoprime for the base C if with N a€“ 1 = 2sd, (2, d) = 1 either Cd = 1, or C2r a‰? 1 (mod N) some r, 0 a‰¤ r < s. It is shown that every arithmetic progression ax+b (x = 0,1, a€|) where a, b are relatively prime integers contains an infinite number of odd strong pseudoprimes for each base C a‰¤ 2.1980 Mathematics subject classification (Amer. Math. Soc.): 10 A 15.
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