Looking for Mathematics Subject Classification
(originally this was a couple of comments, but perhaps it should be an answer)

Section 11: Number Theory is on pp. 4-6 of this current Mathematics Subject Classification (MSC) document. Besides just looking for what seems to be appropriate there (often, however, this requires a much broader knowledge than the specific topic you're looking for), you can look for similar papers and see how they're classified. For example, you can try a google scholar search for "Pythagorean triples", pick a possibly similar paper such as Height and excess of Pythagorean triples, and if you don't have access to it and you don't see any MSC's for it, you can look it up at MR Lookup (freely available), click on the MR number to get MR2126355, at which point you can see "11D09 (20M99)" (11D09 is the primary classification, 20M99 is a secondary classification). Repeat with other papers you find. Thus, in the case of Clifford algebras and Euclid’s parametrization of Pythagorean triples I get 11D09 (11E25 15A66 20H20). It appears (but do some more checks of this nature) that Nate Eldredge (in a comment) was correct -- 11D09 seems an appropriate classification, probably the primary classification.