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A primitive right triangle is a right triangle having integer sides , , and such that , where is the greatest common divisor. The set of values is then known as a primitive Pythagorean triple.

The smallest known area shared by three primitive right triangles is 13123110, corresponding to the triples (4485, 5852, 7373), (1380, 19019, 19069), and (3059, 8580, 9109) (Beiler 1966, p. 127; Gardner 1984, p. 160), as discovered by C. L. Shedd in 1945.

See also

Primitive Pythagorean Triple, Pythagorean Triangle, Pythagorean Triple, Right Triangle

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References

Beiler, A. H. "The Eternal Triangle." Ch. 14 in Recreations in the Theory of Numbers: The Queen of Mathematics Entertains. New York: Dover, 1966.Gardner, M. The Sixth Book of Mathematical Games from Scientific American. Chicago, IL: University of Chicago Press, pp. 160-161, 1984.

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Primitive Right Triangle

Cite this as:

Weisstein, Eric W. "Primitive Right Triangle." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PrimitiveRightTriangle.html

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