A Pythagorean triple (PT) is an ordered triple (a, b, c) that satisfies the Pythagorean equation:
Find an ordered triple (x, y, z) that satisfies the Diophantine equation
where x, y and z are positive integers.
Read this paper http://arxiv.org/pdf/1508.07562.pdf
In the ” Concluding Remark” section:
However, the result in Theorem 2.2 does not generate all almost Pythagorean triples explicitly since we restrict there our PPTs to be of the form:
As a possible extension to this note, we encourage the readers to answer the problem:
“Is there an explicit formula that generates all almost Pythagorean triples?
If none, given two explicit solutions (comes in pair) and , can we possibly device a criterion that determines which one is ideal, perhaps in terms of the number of APT’s being generated?”.