科研之友
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摘要
A set {a(1), a(2), ..., a(m)} of positive integers is called a Diophantine m-tuple if a(i)a(j) + 1 is a perfect square for all 1 <= i < j <= m. In this paper, we show that the form of third element in Diophantine pairs and develop some results which are needed to prove the extendibility of the Diophantine pair {a, b} with some conditions. By using this result, we prove the extendibility of Diophantine pairs {Fk-2Fk+1, F(k-1)F(k+2})and {Fk-2Fk-1, Fk+1Fk+2}, where F-n is the n-th Fibonacci number.
- 出版日期2018
