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Is this all of the possibilities?
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See [http://en.wikipedia.org/wiki/Diophantine_equation Diophantine equations], computer programs [http://tonyforster.blogspot.com/2010/09/turtle-diophantine.html including ones written in TurtleArt] can find all the solutions by trial and error.
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Paste [[File:Turtle Art Activity fraction diophantine.ta |this code]] into Turtle Art to calculate all the possibilities
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This program can be modified for 1/3 and 2/3 and with more work it could be used for the Caacupé abacus.
Is this all of the possibilities?
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See [http://en.wikipedia.org/wiki/Diophantine_equation Diophantine equations], computer programs [http://tonyforster.blogspot.com/2010/09/turtle-diophantine.html including ones written in TurtleArt] can find all the solutions by trial and error.
 
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