A Note on Defining Ideals of Monomial Curves Associated to Primitive Pythagorean Triples

In this survey, we study the defining ideals [Formula: see text] of the space monomial curves [Formula: see text] for primitive Pythagorean triples (PPT) [Formula: see text]. We give a minimal system of generators of [Formula: see text]. Hence, we provide the formula for Frobenius number of a PPT. Additionally, we show that over every field of arbitrary characteristic, there are distinct primitive Pythagorean triples such that their symbolic Rees algebras are noetherian.