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''Pythagorean triple''

Triplets of positive integers $x,y,z$ satisfying the [[Diophantine equations|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====
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<TR><TD valign="top">[a1]</TD> <TD valign="top">  G.H. Hardy,   E.M. Wright,   "An introduction to the theory of numbers" , Oxford Univ. Press  (1979)  pp. Chapt. XIII</TD></TR>
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