Properties of the sequences

Author:
Solomon W. Golomb

Journal:
Math. Comp. **30** (1976), 657-663

MSC:
Primary 10A40; Secondary 94A15

DOI:
https://doi.org/10.1090/S0025-5718-1976-0404129-8

Erratum:
Math. Comp. **38** (1982), 335-336.

Erratum:
Math. Comp. **38** (1982), 335.

MathSciNet review:
0404129

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: For applications to fast finite field transforms, one is interested in the arithmetic of , where the order of the multiplicative group, , is divisible by a high power of 2, and where the multiplicative order of 2 modulo *p* is large. Primes of the form appear well-suited to these objectives. Results are obtained on the divisibility properties of the numbers , and on the exponent of 2 modulo when is prime. Generalizations to various related types of sequences are also considered.

**[1]**C. M. RADER, "Discrete convolutions via Mersenne transforms,"*IEEE Trans. Computers*, v. C-21, 1972, pp. 1269-1273. MR**0438672 (55:11580)****[2]**I. S. REED & T. K. TRUONG, "The use of finite fields to compute convolutions,"*IEEE Trans. Information Theory*, v. IT-21, 1975, pp. 208-213. MR**0406677 (53:10463)****[3]**R. M. ROBINSON, "A report on primes of the form and on factors of Fermat numbers,"*Proc. Amer. Math. Soc.*, v. 9, 1958, pp. 673-681. MR**20**#3097. MR**0096614 (20:3097)****[4]**J. C. MOREHEAD, "Note on the factors of Fermat's numbers,"*Bull. Amer. Math. Soc.*, v. 12, 1906, pp. 449-451. MR**1558370****[5]**E. LEHMER, "Criteria for cubic and quartic residuacity,"*Mathematika*, v. 5, 1958, pp. 20-29. MR**20**#1668. MR**0095162 (20:1668)****[6]**R. M. ROBINSON, "The converse of Fermat's theorem,"*Amer. Math. Monthly*, v. 64, 1957, pp. 703-710. MR**20**#4520. MR**0098057 (20:4520)**

Retrieve articles in *Mathematics of Computation*
with MSC:
10A40,
94A15

Retrieve articles in all journals with MSC: 10A40, 94A15

Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1976-0404129-8

Article copyright:
© Copyright 1976
American Mathematical Society