Pythagorean numbers
From Encyclopedia of Mathematics
Triplets of positive integers 
satisfying 
. Any solution 
to this equation, and consequently all (possibly after switching 
only) Pythagorean numbers, can be expressed as 
, 
, 
, where 
and 
are positive integers 
. The Pythagorean numbers can be interpreted as the sides of a right-angled triangle (cf. Pythagoras theorem).
Comments
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=31584
Pythagorean numbers. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Pythagorean_numbers&oldid=31584
This article was adapted from an original article by BSE-3 (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article