求所有S-丢番图四元对于一组固定的素数S。

IF 0.8 4区数学 Q2 MATHEMATICS

Monatshefte fur Mathematik Pub Date : 2021-01-01 Epub Date: 2021-07-19 DOI:10.1007/s00605-021-01605-w

Volker Ziegler

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引用次数: 0

摘要

给定一个素数的有限集合S和一个m元组(a 1，…，a m)的正整数，我们称m元组为S- diophantine，如果对于每一个1≤i≤j≤m，数量a i a j + 1的素数只来自集合S，我们给出一个实用的算法来求出所有S- diophantine四元组，假设| S | = 3。

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Finding all S-Diophantine quadruples for a fixed set of primes S.

Given a finite set of primes S and an m-tuple $(a_{1}, \dots, a_{m})$ of positive, distinct integers we call the m-tuple S-Diophantine, if for each $1 \leq i < j \leq m$ the quantity $a_{i} a_{j} + 1$ has prime divisors coming only from the set S. For a given set S we give a practical algorithm to find all S-Diophantine quadruples, provided that $| S | = 3$ .

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来源期刊

Monatshefte fur Mathematik 数学-数学

CiteScore

1.60

自引率

11.10%

发文量

155

审稿时长

4-8 weeks

期刊介绍： The journal was founded in 1890 by G. v. Escherich and E. Weyr as "Monatshefte für Mathematik und Physik" and appeared with this title until 1944. Continued from 1948 on as "Monatshefte für Mathematik", its managing editors were L. Gegenbauer, F. Mertens, W. Wirtinger, H. Hahn, Ph. Furtwängler, J. Radon, K. Mayrhofer, N. Hofreiter, H. Reiter, K. Sigmund, J. Cigler. The journal is devoted to research in mathematics in its broadest sense. Over the years, it has attracted a remarkable cast of authors, ranging from G. Peano, and A. Tauber to P. Erdös and B. L. van der Waerden. The volumes of the Monatshefte contain historical achievements in analysis (L. Bieberbach, H. Hahn, E. Helly, R. Nevanlinna, J. Radon, F. Riesz, W. Wirtinger), topology (K. Menger, K. Kuratowski, L. Vietoris, K. Reidemeister), and number theory (F. Mertens, Ph. Furtwängler, E. Hlawka, E. Landau). It also published landmark contributions by physicists such as M. Planck and W. Heisenberg and by philosophers such as R. Carnap and F. Waismann. In particular, the journal played a seminal role in analyzing the foundations of mathematics (L. E. J. Brouwer, A. Tarski and K. Gödel). The journal publishes research papers of general interest in all areas of mathematics. Surveys of significant developments in the fields of pure and applied mathematics and mathematical physics may be occasionally included.