The Distribution of Residues in a Sequence Satisfying a Linear Recursion Relation

Morgan Ward
1931 Transactions of the American Mathematical Society  
§ As far as I am aware, this problem has not been explicitly considered for difference equations of order greater than two. In a paper which has already appeared in these Transactions I have considered the problem of determining t, given P, Q, R, Wo, Wi, Wï and m. 166 License or copyright restrictions may apply to redistribution; see http://www.ams.org/journal-terms-of-use * In connection with the first problem, probably the best known result is that if Wo = 3, WX=P, Wi=P2-2Q and p is a prime,
more » ... and p is a prime, then Wn = Wnp= Wn? mod p. In §8 of this paper I shall give several new results of a similar character. t We shall omit the words "modulo p" when no confusion can arise.
doi:10.2307/1989465 fatcat:xonugo43djaavhezms2rsk6gom