Generating All Coprime Pairs

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Two integers are said to be coprime (or relatively prime) if they do not share a common divisor different than 1. For instance, 4 and 9 are coprime (no common divisor except 1), but 12 and 15 are not (common divisor 3). The plot shows generations of coprime pairs , starting from and , where three new pairs are produced at each step: , , and . The resulting triplets can be arranged in two complete ternary trees. The procedure described here generates all coprime pairs without repetition; the colors represent the different generations.

Contributed by: Enrique Zeleny (September 2012)
Open content licensed under CC BY-NC-SA


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Reference

[1] Wikipedia. "Coprime Integers." (Sep 26, 2012) en.wikipedia.org/wiki/Coprime_integers.



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