منابع مشابه
Diophantine Equations Involving Arithmetic Functions of Factorials
DIOPHANTINE EQUATIONS INVOLVING ARITHMETIC FUNCTIONS OF FACTORIALS Daniel M. Baczkowski We examine and classify the solutions to certain Diophantine equations involving factorials and some well known arithmetic functions. F. Luca has showed that there are finitely many solutions to the equation:
متن کاملDiophantine Approximation by Primes
We show that whenever δ > 0 and constants λi satisfy some necessary conditions, there are infinitely many prime triples p1, p2, p3 satisfying the inequality |λ0 + λ1p1 + λ2p2 + λ3p3| < (max pj)−2/9+δ. The proof uses Davenport–Heilbronn adaption of the circle method together with a vector sieve method. 2000 Mathematics Subject Classification. 11D75, 11N36, 11P32.
متن کاملDiophantine m-tuples for primes
In this paper, we show that if p is a prime and ifA = {a1, a2, . . . , am} is a set of positive integers with the property that aiaj +p is a perfect square for all 1 ≤ i < j ≤ m, then m < 3 · 2168. More generally, when p is replaced by a squarefree integer n, the inequality m ≤ f(ω(n)) holds with some function f , where ω(n) is the number of prime divisors of n. We also give upper bounds for m ...
متن کاملDiophantine approximation and Diophantine equations
The first course is devoted to the basic setup of Diophantine approximation: we start with rational approximation to a single real number. Firstly, positive results tell us that a real number x has “good” rational approximation p/q, where “good” is when one compares |x − p/q| and q. We discuss Dirichlet’s result in 1842 (see [6] Course N◦2 §2.1) and the Markoff–Lagrange spectrum ([6] Course N◦1...
متن کاملDiophantine Approximations, Diophantine Equations, Transcendence and Applications
This article centres around the contributions of the author and therefore, it is confined to topics where the author has worked. Between these topics there are connections and we explain them by a result of Liouville in 1844 that for an algebraic number α of degree n ≥ 2, there exists c > 0 depending only on α such that | α− p q |> c qn for all rational numbers p q with q > 0. This inequality i...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annales Polonici Mathematici
سال: 1966
ISSN: 0066-2216,1730-6272
DOI: 10.4064/ap-18-3-315-321