24 citations · 99 across the 9 of their papers we have counts for
12 papers · 1 filter
Around Pelikan's conjecture on very odd sequences
Pieter Moree, Patrick Sole
Very odd sequences were introduced in 1973 by J. Pelikan who conjectured that there were none of length >=5. This conjecture was disproved by MacWilliams and Odlyzko in 1977 who pr…
On the distribution of the order and index of g(mod p) over residue classes II
Pieter Moree
For a fixed rational number g different from -1,0,1 and integers a and d the set N_g(a,d) of primes p for which the order of g(mod p) is congruent to a(mod d) is considered. It is…
Some Heuristics and Results for Small Cycles of the Discrete Logarithm
Joshua Holden, Pieter Moree
Brizolis asked the question: does every prime p have a pair (g,h) such that h is a fixed point for the discrete logarithm with base g? The first author previously extended this que…
Asymptotically exact heuristics for prime divisors of a^k+b^k
Pieter Moree
Let N_{a,b}(x) count the number of primes p<=x with p dividing a^k+b^k for some k>=1. It is known that asymptotically N_{a,b}(x) grows like c(a,b)x/log x for some rational number c…
Value distribution of Ramanujan sums and of cyclotomic polynomial coefficients
Pieter Moree, Huib Hommersom
The Ramanujan sum c_n(k) and a_n(k), the kth coefficient of the nth cyclotomic polynomial, are completely symmetric expressions in terms of primitive nth roots of unity. For fixed…
New Conjectures and Results for Small Cycles of the Discrete Logarithm
Joshua Holden, Pieter Moree
Brizolis asked the question: does every prime p have a pair (g,h) such that h is a fixed point for the discrete logarithm with base g? The first author previously extended this que…