Results 81 to 90 of about 1,693 (108)
Thirty-Six Unsolved Problems in Number Theory [PDF]
arXiv, 2000 Partially or totally unsolved questions in number theory and geometry especially, such as coloration problems, elementary geometric conjectures, partitions, generalized periods of a number, length of a generalized period, arithmetic and geometric progressions are exposed.
arxiv
arXiv, 2002 Studying Fermat sequence we can simply find infinitely many other rapidly growing sequences of similar properties. On the other hand this approach allows us simple construction of such sequences.
arxiv
Some remarks on a paper by L. Carlitz [PDF]
arXiv, 2005 We study a family of orthogonal polynomials which generalizes a sequence of polynomials considered by L. Carlitz. We show that they are a special case of the Sheffer polynomials and point out some interesting connections with certain Sobolev orthogonal polynomials.
arxiv
Simple closed form Hankel transforms based on the central coefficients of certain Pascal-like triangles [PDF]
arXiv, 2006 We study the Hankel transforms of sequences related to the central coefficients of a family of Pascal-like triangles. The mechanism of Riordan arrays is used to elucidate the structure of these transforms.
arxiv
Somos Sequence Near-Addition Formulas and Modular Theta Functions [PDF]
arXiv, 2007 We have discovered conjectural near-addition formulas for Somos sequences. We have preliminary evidence suggesting the existence of modular theta functions.
arxiv
A new formula for the coefficients of Gaussian polynomials
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2019 We deduce exact integral formulae for the coefficients of Gaussian, multinomial and Catalan polynomials. The method used by the authors in the papers [2, 3, 4] to prove some new results concerning cyclotomic and polygonal polynomials, as well as some of ...
Andrica Dorin, Bagdasar Ovidiu
doaj +1 more source
Difference sets and shifted primes [PDF]
arXiv, 2007 We show that if A is a subset of {1, ..., n} such that it has no pairs of elements whose difference is equal to p-1 with p a prime number, then the size of A is O(n(loglog n)^(-clogloglogloglog n)) for some positive constant c.
arxiv
On some properties on bivariate Fibonacci and Lucas polynomials [PDF]
arXiv, 2007 In this paper we generalize to bivariate polynomials of Fibonacci and Lucas, properties obtained for Chebyshev polynomials. We prove that the coordinates of the bivariate polynomials over appropriate basis are families of integers satisfying remarkable recurrence relations.
arxiv
A Study on Dual Hyperbolic Fibonacci and Lucas Numbers
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2019 In this study, the dual-hyperbolic Fibonacci and dual-hyperbolic Lucas numbers are introduced. Then, the fundamental identities are proven for these numbers.
Cihan Arzu +3 more
doaj +1 more source
Greedy and quasi-greedy expansions in non-integer bases [PDF]
arXiv, 2007 We generalize several theorems of R\'enyi, Parry, Dar\'oczy and K\'atai by characterizing the greedy and quasi-greedy expansions in non-integer bases.
arxiv