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math.NT2003
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…
math.NT2003★ 14 cited
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…
math.NT2003
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…