On the (3N+1)-conjecture
On the behavior of a variant of Hofstadter's -sequence.
On the Collatz conjecture
We propose two conjectures which imply the Collatz conjecture. We give a numerical evidence for the second conjecture.
On the composite Lehmer numbers with prime indices, III
On the cycle structure of linear recurring sequences.
On the density of some sets of primes connected with cyclotomic polynomials
On the Diophantine equation ax...+bx...y+cy...=d and pure powers in recurrence sequences.
On the Diophantine equation for third order linear recurring sequences.
On the Diophantine equation
In this study, we determine when the Diophantine equation has an infinite number of positive integer solutions and for Moreover, we give all positive integer solutions of the same equation for in terms of generalized Fibonacci sequence. Lastly, we formulate a conjecture related to the Diophantine equation .
On the expansion of Fibonacci and Lucas polynomials.
On the multiplicities of binary complex recurrences
On the number of subgroups of given index in the modular group.
On the period of the continued fraction for values of the square root of power sums
On the quartic character of quadratic units.
On the resolution of index form equations in dihedral quartic number fields.
On the set of numbers {14, 22, 30, 42, 90}
On the sumset of the primes and a linear recurrence
Romanoff (1934) showed that integers that are the sum of a prime and a power of 2 have positive lower asymptotic density in the positive integers. We adapt his method by showing more generally the existence of a positive lower asymptotic density for integers that are the sum of a prime and a term of a given nonconstant nondegenerate integral linear recurrence with separable characteristic polynomial.
On the zeros of linear recurrence sequences
On two classes of polynomials in number-theory
On two theorems of Gelfond and some of their applications