Sylvester Cyclotomic Number
المؤلف:
Ribenboim, P.
المصدر:
The New Book of Prime Number Records. New York: Springer-Verlag
الجزء والصفحة:
...
7-11-2020
899
Sylvester Cyclotomic Number
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
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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