We show that for infinitely many square-free integers q there exist infinitely many triples of rational numbers {a, b, c} such that a^2 + q, b^2 + q, c^2 + q, ab + q, ac + q and bc + q are squares of rational numbers.

中文翻译：

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强有理丢番图 D(q)-三元组

我们证明对于无限多个无平方整数 q 存在无限多个有理数三元组 {a, b, c} 使得 a^2 + q, b^2 + q, c^2 + q, ab + q, ac + q 和 bc + q 是有理数的平方。