Golomb's conjectures and related problems (Q1902240)
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scientific article; zbMATH DE number 817773
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Golomb's conjectures and related problems |
scientific article; zbMATH DE number 817773 |
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Golomb's conjectures and related problems (English)
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16 November 1995
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The conjectures of \textit{S. Golomb} [J. Comb. Theory, Ser. A 37, 13-21 (1984; Zbl 0547.05020)]\ concern the representability of elements of a finite field as sums of two primitive elements. Using tools from analytic number theory, the author obtains an asymptotic formula for the number of such representations in the special case of finite fields \(GF(p)\), \(p\) an odd prime. As a corollary, the Golomb conjectures hold in \(GF(p)\) if \(p-1\) does not have too many prime divisors.
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representability
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sums of two primitive elements
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asymptotic formula
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Golomb conjectures
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