求所有S-丢番图四元对于一组固定的素数S。

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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