For a compact Kähler manifold X and a strongly primitive automorphism g of positive entropy, it is shown that X has at most ρ(X) of g-periodic prime divisors. When X is a projective threefold, every prime divisor containing infinitely many g-periodic curves, is shown to be g-periodic (a result in the spirit of the Dynamic Manin-Mumford conjecture as in [17]).

We develop a mechanism for classication of isomorphism types of non-trivial semisimple Hopf algebras whose group of grouplikes G(H) is abelian of prime index p which is the smallest prime divisor of |G(H)|. We describe structure of the second cohomology group of extensions of kCp by k G where Cp is a cyclic group of order p and G a finite abelian group. We carry out an explicit classification f...

Proof: For a contradiction, assume there are finitely many, p1, . . . , pn. Construct N = Πi=1pi. Then for any i, pi does not divide N + 1, so N + 1 is not divisible by any prime. This is a contradiction, since all numbers ≥ 2 are divisible by some prime. (This can be easily proved by induction.) Definition 1.4. We say that two numbers, a, and b are congruent mod m, or a ≡ b mod m if m | b− a. ...

We discuss the numbers in the title, and in particular whether the minimum period of the Bell numbers modulo a prime p can be a proper divisor of Np = (pp − 1)/(p− 1). It is known that the period always divides Np. The period is shown to equal Np for most primes p below 180. The investigation leads to interesting new results about the possible prime factors of Np. For example, we show that if p...

The formula mentioned in the title is proved. Introduction Let S, T be complete nonsingular surfaces over an algebraically closed field k of any characteristic, and let h : T → S be a finite separable morphism of degree n. We establish a formula that expresses the Euler characteristic (understood as the degree of the second Chern class ∫ c2,T ) of T via the Euler characteristic of S and some lo...

the estimation of (1.1) for ξ = 1 is related to the location of the zeros of ζ, which is the classical approach to the prime number theorem, and for multiplicative ξ in general the problem can be related to the properties of a corresponding L-function in a similar way. (Chapter 5 of [13] contains a comprehensive discussion of this and related issues). A shift in the argument of ξ destroys the m...

A positive integer is called a (Ore’s) harmonic number if its positive divisors have integral harmonic mean. Ore conjectured that every harmonic number greater than 1 is even. If Ore’s conjecture is true, there exist no odd perfect numbers. In this paper, we prove that every odd harmonic number greater than 1 must be divisible by a prime greater than 105.

We study some arithmetic properties of the Ramanujan function τ(n), such as the largest prime divisor P(τ(n)) and the number of distinct prime divisors ω(τ(n)) of τ(n) for various sequences of n. In particular, we show that P(τ(n)) ≥ (logn)33/31+o(1) for infinitely many n, and P(τ(p)τ(p2)τ(p3)) > (1+o(1)) log log p log log log p loglog log log p for every prime p with τ(p) 6= 0.

continue to investigate the problem of the existence of a Hamilton connected cubic (m,n)-metacirculant graphs. We show that a connected cubic (m,n)-metacirculant graph G = MC(m, n, a, So, ,.., has Hamilton cycle if either a 2 == 1 (mod n) or in the case of an odd number f.L one of the numbers (a 1) or a + a 2 _ ... ajJ.-2 + ajJ.-l) relatively to n. As a corollary of results we obtain that every...

The performance analysis of Hyperelliptic Curve Cryptosystems (HECC) over prime fields (Fp) of genus 5 and 6 are discussed in this paper. We have implemented a HECC system of genus 5 & 6 in a Intel Pentium III Celeron Processor @ 933 MHz speed with 256 MB RAM in Java 1.5. We have also compared their efficiency on the parameters of time taken for divisor generation, key generation, encryption an...