An isomorphism between linear recurring sequences and algebraic rings

Abstract

The notation and terminology of this paper are in agreement with Ward [l 1 ] for the most part.I use "period" following Engstrom rather than Ward's "characteristic number."* Ward [ll], p. 622, gives some information which shows that the defect can be greater than unity only in certain rare cases.The determination of the defect is the generalization of the (unsolved) problem of the Fermt quotients (ap~l-l)/p.