| Popis: |
For each seed s =(s 1 ,s 2 ,…,s n ) of elements si chosen from the ring Z m of integers modulo m, the infinite sequence S = S (m, s )=(s k :k∈ N ) satisfying sn+k=sk+sk+1 (addition in Z m ) for every positive integer k is the (m,n) chain addition sequence generated by the seed s. We investigate the maximal period, Ln(m), of chain addition cycles with seed length n (modulo m). The general problem is reduced to finding Ln(pk) for primes p and it is shown that if Ln(p2)≠Ln(p), then Ln(pk)=pk−1Ln(p) for positive integers k. Further, conditions guaranteeing that Ln(p2)≠Ln(p) are given. |
