Asymptotically exact heuristics for prime divisors of the sequence .
Convoluted convolved Fibonacci numbers.
On a class of ternary inclusion-exclusion polynomials.
An interval result for the number field v(x,y) function.
A generalization of the Buchstab equation.
On the number of y-smooth natural numbers ... representable as a sum of two integer squares.
On the prime density of Lucas sequences
The density of primes dividing at least one term of the Lucas sequence , defined by and for , with an arbitrary integer, is determined.
Uniform distribution of primes having a prescribed primitive root
On the divisors of
On arithmetic progressions having only few different prime factors in comparison with their length
Prime divisors of the Lagarias sequence
We solve a 1985 challenge problem posed by Lagarias [5] by determining, under GRH, the density of the set of prime numbers that occur as divisor of some term of the sequence defined by the linear recurrence and the initial values and . This is the first example of a ænon-torsionÆ second order recurrent sequence with irreducible recurrence relation for which we can determine the associated density of prime divisors.
Prime divisors of Lucas sequences
On Robin’s criterion for the Riemann hypothesis
Robin’s criterion states that the Riemann Hypothesis (RH) is true if and only if Robin’s inequality is satisfied for , where denotes the Euler(-Mascheroni) constant. We show by elementary methods that if does not satisfy Robin’s criterion it must be even and is neither squarefree nor squarefull. Using a bound of Rosser and Schoenfeld we show, moreover, that must be divisible by a fifth power . As consequence we obtain that RH holds true iff every natural number divisible by a fifth power...
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