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.
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Do Van Kien (2024) studied this question.
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