New posts in Pythagorean Triples

Are there finitely many Pythagorean triples whose smallest two numbers differ by 1?

At least one member of a pythagorean triple is even

Derivation of Pythagorean Triple General Solution Starting Point:

For which $n$ are there primitive Pythagorean triples with legs of lengths $a$ and $a+n$?

Assistance with understanding parent/child relationships in Pythagorean Triples