论文标题
寻找所有$ s $ dioophantine Quadrples for固定的Primes $ S $
Finding all $S$-Diophantine quadruples for a fixed set of primes $S$
论文作者
论文摘要
Given a finite set of primes $S$ and a $m$-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 $a_ia_j+1$ has prime divisors coming only from the set $S$.对于给定的$ s $，我们给出一种实用算法，以找到所有$ s $ dioophantine Quadruples，但前提是$ | s | = 3 $。
Given a finite set of primes $S$ and a $m$-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 $a_ia_j+1$ 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 $|S|=3$.
