The distribution of residues in a sequence satisfying a linear recursion relation
Morgan Ward · Transactions of the American Mathematical Society · 1931
§ 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. * 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, 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.* For the properties of Galois fields which are assumed here, see Dickson, Linear Groups, Leipzig, 1901.