Memoirs of the American Mathematical Society 1995; 102 pp; softcover Volume: 115 ISBN10: 0821826107 ISBN13: 9780821826102 List Price: US$42 Individual Members: US$25.20 Institutional Members: US$33.60 Order Code: MEMO/115/551
 A result due to Hasse says that, on average, 17 out of 24 consecutive primes will divide a number in the sequence \(U_n = 2^n+1\). There are few sequences of integers for which this relative density can be computed exactly. In this work, Ballot links Hasse's method to the concept of the group associated with the set of secondorder recurring sequences having the same characteristic polynomial and to the concept of the rank of prime division in a Lucas sequence. This combination of methods and ideas allows the establishment of new density results. Ballot also shows that this synthesis can be generalized to recurring sequences of any order, for which he also obtains new density results. All the results can be shown to be in close agreement with the densities computed using only a small set of primes. This wellwritten book is fairly elementary in nature and requires only some background in Galois theory and algebraic number theory. Readership Graduate students, mathematicians, and possibly computer scientists with an interest in number theory. Table of Contents  Introduction
 General preliminaries
 Background material
 More about recurring sequences of order two
 A study of the cubic case
 Study of the general case \(m\geq 2\)
 Appendix Alist of theorems
 Appendix Blist of symbols
 References
