We examine iteration graphs of the squaring function on the rings ℤ/nℤ when n = 2kp, for p a Fermat prime. We describe several invariants associated to these graphs and use them to prove that the… Expand

Two classical problems In elementary number theory appear, at first, to be unrelated. The first, posed by D. H. Lehmer in [7], asks whether there is a composite integer N such that </>{N) divides… Expand

The concept of sequence stability generalizes the idea of uniform distribution. A sequence is p-stable if the set of residue frequencies of the sequence reduced modulo p r is eventually constant as a… Expand

The authors describe a technique for characterizing stable two-term recurrence sequences and apply the technique to identify stable sequences that were not previously known to be stable.

One approach to the study of the distributions of residues of second-order recurrence sequences (wn) modulo powers of a prime p is to identify and examine subsequences w% = wn+tmj that are themselves… Expand

The concept of sequence stability generalizes the idea of uniform distribution. A sequence is p-stable if the set of residue frequencies of the sequence reduced modulo pr is eventually constant as a… Expand

Consider the two-term recurrence sequence {u n} defined by u o = 0, u 1 = 1 and for all n ≥ 2, where a and b are fixed (rational) integers. Let p be a fixed odd prime such that
$$ p{\text{X}}ab(a2… Expand