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Pythagorean numbers

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2020 Mathematics Subject Classification: Primary: 11D09 [MSN][ZBL]

Pythagorean triple

Triplets of positive integers satisfying the Diophantine equation x^2+y^2=z^2. After removing a common factor, and possibly switching x,y, any solution (x,y,z) to this equation, and consequently all Pythagorean numbers, can be obtained as x=a^2-b^2, y=2ab, z=a^2+b^2, where a and b are positive integers (a>b). The Pythagorean numbers can be interpreted as the sides of a right-angled triangle (cf. Pythagoras theorem).

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References

[a1] G.H. Hardy, E.M. Wright, "An introduction to the theory of numbers" , Oxford Univ. Press (1979) pp. Chapt. XIII
How to Cite This Entry:
Pythagorean numbers. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Pythagorean_numbers&oldid=39945
This article was adapted from an original article by BSE-3 (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article