In this paper, we define new kinds of Fibonacci numbers, which generalize both Fibonacci, Jacobsthal, Narayana numbers and p-numbers in the distance sense, using definition a between by recurrence relation according to parameter k. Tiling combinatorial interpretations these are presented, explicit formulas that allow us calculate nth number given. Also, their generating functions obtained sums ...

Let p be prime and let GF (p) be the finite field with p elements. In this note we investigate the arithmetic properties of the Gaussian hypergeometric functions 2F1(x) =2 F1 „ φ, φ | x « and 3F2(x) =3 F2 „ φ, φ, φ , | x « where φ and respectively are the quadratic and trivial characters of GF (p). For all but finitely many rational numbers x = λ, there exist two elliptic curves 2E1(λ) and 3E2(...

There have been many reports on the properties of various polynomial sequences and their generalizations (see, e.g., [1], [3], [4], [5], [6], and [9] and the references therein). In this paper we shall try to treat some polynomial sequences by virtue of the line-sequential formalism developed earlier. To this end? we choose [9] as the guide of our endeavor and obtain some results of a different...

is true. The exponent c3 can be reduced by Selberg's improvement of Brun's method, but it seems hopeless at present to decide about (3) . Jacobsthal also informed me that for r <_ 10 the value of C(r) is determined by n,.= 2, 3 . . . . p,., the p's being the consecutive primes, and that this perhaps holds for all values of r . Possibly the value of g(n,.') for n,'=n =1p,á+1 is already considera...