engleski

The extendibility of Diophantine pairs I : the general case

Let $a$ and $b$ be positive integers with $a < b$, such that $ab+1$ is a perfect square. In this paper we give an upper bound for the minimal positive integer $c$ such that ${; ; ; a, b, c, d}; ; ; $ is the set of positive integers which has the property that the product of any two of its elements increased by $1$ is a perfect square and $d\neq a+b+c+2(abc\pm\sqrt{; ; ; (ab+1)(ac+1)(bc+1)}; ; ; )$.

Diophantine tuples ; simultaneous Diophantine equations

nije evidentirano