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Algebraic structures of some sets of Pythagorean triples. II. (English) Zbl 1119.13301

Summary: A natural bijection from \(\mathbb{Z}^2\) to the set of all Pythagorean triples \(\mathcal P=\{(a,b,c)\in \mathbb{Z}^3 : a^2+b^2=c^2 \}\) is given. Consequently, all algebraic structures are carried in a natural way to \(\mathcal P\). This solves the problem of defining ring operations under which \(\mathcal P\) is essentially a different ring than the one constructed by B. Dawson.
[For part I, see Missouri J. Math. Sci. 12, No. 1 (2000; Zbl 1119.13300).]

MSC:

13A99 General commutative ring theory
11D09 Quadratic and bilinear Diophantine equations

Citations:

Zbl 1119.13300
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