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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Properties of the sequences $ 3\cdot 2\sp{n}+1$


Author: Solomon W. Golomb
Journal: Math. Comp. 30 (1976), 657-663
MSC: Primary 10A40; Secondary 94A15
Erratum: Math. Comp. 38 (1982), 335-336.
Erratum: Math. Comp. 38 (1982), 335.
MathSciNet review: 0404129
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Abstract: For applications to fast finite field transforms, one is interested in the arithmetic of $ GF(p)$, where the order of the multiplicative group, $ \varphi (p) = p - 1$, is divisible by a high power of 2, and where the multiplicative order of 2 modulo p is large. Primes of the form $ 3 \bullet {2^n} + 1$ appear well-suited to these objectives. Results are obtained on the divisibility properties of the numbers $ {A_n} = 3 \bullet {2^n} + 1$, and on the exponent of 2 modulo $ {A_n}$ when $ {A_n}$ is prime. Generalizations to various related types of sequences are also considered.


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DOI: http://dx.doi.org/10.1090/S0025-5718-1976-0404129-8
PII: S 0025-5718(1976)0404129-8
Article copyright: © Copyright 1976 American Mathematical Society