Properties of the sequences
Author:
Solomon W. Golomb
Journal:
Math. Comp. 30 (1976), 657663
MSC:
Primary 10A40; Secondary 94A15
Erratum:
Math. Comp. 38 (1982), 335336.
Erratum:
Math. Comp. 38 (1982), 335.
MathSciNet review:
0404129
Fulltext 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 wellsuited 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]
Charles
M. Rader, Discrete convolutions via Mersenne transforms, IEEE
Trans. Computers C21 (1972), 1269–1273. MR 0438672
(55 #11580)
 [2]
Irving
S. Reed and T.
K. Truong, The use of finite fields to compute convolutions,
IEEE Trans. Information Theory IT21 (1975),
208–213. MR 0406677
(53 #10463)
 [3]
Raphael
M. Robinson, A report on primes of the form
𝑘⋅2ⁿ+1 and on factors of Fermat numbers, Proc. Amer. Math. Soc. 9 (1958), 673–681. MR 0096614
(20 #3097), http://dx.doi.org/10.1090/S00029939195800966147
 [4]
J.
C. Morehead, Note on the factors of Fermat’s
numbers, Bull. Amer. Math. Soc.
12 (1906), no. 9,
449–451. MR
1558370, http://dx.doi.org/10.1090/S000299041906013714
 [5]
Emma
Lehmer, Criteria for cubic and quartic residuacity,
Mathematika 5 (1958), 20–29. MR 0095162
(20 #1668)
 [6]
Raphael
M. Robinson, The converse of Fermat’s theorem, Amer.
Math. Monthly 64 (1957), 703–710. MR 0098057
(20 #4520)
 [1]
 C. M. RADER, "Discrete convolutions via Mersenne transforms," IEEE Trans. Computers, v. C21, 1972, pp. 12691273. MR 0438672 (55:11580)
 [2]
 I. S. REED & T. K. TRUONG, "The use of finite fields to compute convolutions," IEEE Trans. Information Theory, v. IT21, 1975, pp. 208213. 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. 673681. 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. 449451. MR 1558370
 [5]
 E. LEHMER, "Criteria for cubic and quartic residuacity," Mathematika, v. 5, 1958, pp. 2029. MR 20 #1668. MR 0095162 (20:1668)
 [6]
 R. M. ROBINSON, "The converse of Fermat's theorem," Amer. Math. Monthly, v. 64, 1957, pp. 703710. MR 20 #4520. MR 0098057 (20:4520)
Similar Articles
Retrieve articles in Mathematics of Computation
with MSC:
10A40,
94A15
Retrieve articles in all journals
with MSC:
10A40,
94A15
Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197604041298
PII:
S 00255718(1976)04041298
Article copyright:
© Copyright 1976
American Mathematical Society
