Editing Pell number (section)

== Pythagorean triples ==
[[Image:Pell right triangles.svg|thumb|300px|Integer right triangles with nearly equal legs, derived from the Pell numbers.]]
If a [[right triangle]] has integer side lengths ''a'', ''b'', ''c'' (necessarily satisfying the [[Pythagorean theorem]] {{nowrap|1=''a''<sup>2</sup> + ''b''<sup>2</sup> = ''c''<sup>2</sup>}}), then (''a'',''b'',''c'') is known as a [[Pythagorean triple]]. As Martin (1875) describes, the Pell numbers can be used to form Pythagorean triples in which ''a'' and ''b'' are one unit apart, corresponding to right triangles that are nearly isosceles. Each such triple has the form
:<math>\left(2P_{n}P_{n+1}, P_{n+1}^2 - P_{n}^2, P_{n+1}^2 + P_{n}^2=P_{2n+1}\right).</math>
The sequence of Pythagorean triples formed in this way is
:(4,3,5), (20,21,29), (120,119,169), (696,697,985), …