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Date: 22-4-2020
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Date: 6-2-2020
585
Date: 28-5-2020
624
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Given a Lucas sequence with parameters and , discriminant , and roots and , the Sylvester cyclotomic numbers are
(1) |
where
(2) |
is a primitive root of unity and the product is over all exponents relatively prime to such that .
For small , the first few values are
(3) |
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(4) |
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(5) |
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(6) |
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(7) |
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(8) |
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(9) |
These numbers satisfy
(10) |
where as usual .
Ward (1954) gave a primality test involving these numbers.
REFERENCES:
Ribenboim, P. The New Book of Prime Number Records. New York: Springer-Verlag, p. 82, 1989.
Ward, M. "Prime Divisors of Second Order Recurring Sequences." Duke Math. J. 21, 607-614, 1954.
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