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ON THE MINIMAL NUMBER OF SMALL ELEMENTS GENERATING FINITE PRIME FIELDS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 96 / Issue 2 / October 2017
- Published online by Cambridge University Press:
- 17 August 2017, pp. 177-184
- Print publication:
- October 2017
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- Article
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- You have access
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In this note, we give an upper bound for the number of elements from the interval
$[1,p^{1/4\sqrt{e}+\unicode[STIX]{x1D716}}]$ necessary to generate the finite field 
$\mathbb{F}_{p}^{\ast }$ with 
$p$ an odd prime. The general result depends on the distribution of the divisors of 
$p-1$ and can be used to deduce results which hold for almost all primes.
