On non-congruent numbers with 1 modulo 4 prime factors

نویسندگان
چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

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 کامل

Families 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 کامل

The Least Prime Congruent to One Modulo n

It is known that there are infinitely many primes ≡ 1 (modn) for any integer n > 1. In this paper, we use an elementary argument to prove that the least such prime satisfies p ≤ 2 − 1, where φ is the Euler totient function.

متن کامل

1 3 M ay 1 99 4 Average kissing numbers for non - congruent sphere packings

(The appearance of the number of the beast in the lower bound is purely coincidental.) The supremal average kissing number k is defined in any dimension, as are kc, the supremal average kissing number for congruent ball packing, and ks, the maximal kissing number for a single ball surrounded by congruent balls with disjoint interiors. (Clearly, kc ≤ k and kc ≤ ks.) It is interesting that k is a...

متن کامل

Optimal (9v, 4, 1) optical orthogonal codes with v a product of primes congruent to 1 modulo 4

Optimal (9p, 4, 1) optical orthogonal codes are constructed for all primes p congruent to 1 modulo 4. Direct constructions with explicit codewords are presented for the case p ≡ 13 mod 24, and Weil’s theorem on character sums is used to settle the cases p ≡ 1, 5, 17 mod 24. By applying a known recursive construction, optimal (9v, 4, 1) and (45v, 4, 1) optical orthogonal codes are obtained for a...

متن کامل

ذخیره 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: Science China Mathematics

سال: 2013

ISSN: 1674-7283,1869-1862

DOI: 10.1007/s11425-013-4705-y