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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.
Do Van Kien (Sat,) studied this question.