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Is there a way to determine the form of all rational solutions to the equation $a^2+b^2=1$?

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    Clear denominators to reduce to the problem of finding all pythagorean triples.2011-11-28
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    Notice that this is the same as integer solutions to $a^2+b^2=c^2$. A full statement of the result and proof can be found on wikipedia: http://en.wikipedia.org/wiki/Pythagorean_triple#Generating_a_triple2011-11-28

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