Abstract
Aigner has defined elite primes as primes p such that all but finitely many of Fermat numbers F(n) = 22n + 1, n = 0, 1, 2..., are quadratic nonresidues modulo p. Since the sequence of Fermat numbers is eventually periodic modulo any p with at most p distinct elements in the image, both the period length tp and the number of arithmetic operations modulo p to test p for being elite are also bounded by p. We show that tp = O(p3/4), in particular improving the estimate tp ≤ (p+1)/4 of Müller and Reinhart in 2008. The same bound O(p3/4) also holds for testing anti-elite primes.
Original language | English |
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Pages (from-to) | 1-5 |
Number of pages | 5 |
Journal | Journal of Integer Sequences |
Volume | 14 |
Issue number | 1 |
Publication status | Published - 2011 |