Since for every odd prime "p", "p" divides "ap" if and only if "p" is congruent to 1 mod 4, and since "p" divides the denominator of th Bernoulli number for every odd prime "p", so for any odd prime "p", "p" cannot divide "a""p"−1. Besides, if and only if an odd prime "p" divides "an" (and 2"p" does not divide "n"), then "p" also divides "a""n"+"k"("p"−1) (if 2"p" divides "n", then the sentence should be changed to ""p" also divides "a""n"+2"kp"". In fact, if 2"p" divides "n" and does not divide "n", then "p" divides "a""n".) for every integer "k" (a condition is must be > 1). For example, since 19 divides "a"11 and does not divide 11, so 19 divides "a"18"k"+11 for all "k". Thus, the definition of irregular pair , "n" should be at most .