The extensibility of Diophantine pairs {k−1,k+1}

By Yasutsugu Fujita. 2008

79 citations recorded by the source corpus.

Abstract A set of m distinct positive integers { a 1 , … , a m } is called a Diophantine m-tuple if a i a j + 1 is a square for each 1 ⩽ i j ⩽ m . In this paper, we show that for each integer k ⩾ 2 the Diophantine pair { k − 1 , k + 1 } cannot be extended to a Diophantine quintuple.

Subfields: Computer Vision and Pattern Recognition, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/94a12ad32d4aee2129abbcafc29e07aadfd78123

Citations in the corpus

• There is no Diophantine quintuple (2016, unknown): “References { k − 1 , k + 1 , 4 k [13] { 1, 3 [19] { k − 1 , k + 1 [24, 4] { a, b with b a + 4 √ a [23] { k, 4 k ± 4 [23, 28] { 1 , b with b − 1 be prime [32] Table 1.”