منابع مشابه
Congruent numbers with many prime factors.
Mohammed Ben Alhocain, in an Arab manuscript of the 10th century, stated that the principal object of the theory of rational right triangles is to find a square that when increased or diminished by a certain number, m becomes a square [Dickson LE (1971) History of the Theory of Numbers (Chelsea, New York), Vol 2, Chap 16]. In modern language, this object is to find a rational point of infinite ...
متن کاملCarmichael Numbers With Three Prime Factors
A Carmichael number (or absolute pseudo-prime) is a composite positive integer n such that n|an − a for every integer a. It is not difficult to prove that such an integer must be square-free, with at least 3 prime factors. Moreover if the numbers p = 6m + 1, q = 12m + 1 and r = 18m + 1 are all prime, then n = pqr will be a Carmichael number. However it is not currently known whether there are i...
متن کاملFamilies of Non-θ-congruent Numbers with Arbitrarily Many Prime Factors
The concept of θ-congruent numbers was introduced by Fujiwara [Fu97], who showed that for primes p ≡ 5, 7, 19 (mod 24), p is not a π/3-congruent number. In this paper we show the existence of two infinite families of composite non-π/3-congruent numbers and non-2π/3-congruent numbers, obtained from products of primes which are congruent to 5 modulo 24 and to 13 modulo 24 respectively. This is ac...
متن کاملDensity of Carmichael numbers with three prime factors
We get an upper bound ofO(x5/14+o(1)) on the number of Carmichael numbers ≤ x with exactly three prime factors.
متن کاملDensity of Carmichael Numbers with Three Prime Factors 1707
We get an upper bound of O(x 5=14+o(1)) on the numberof Carmichael numbers x with exactly three prime factors.
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2008
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2008.03.010