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integer triangle
An integer triangle or integral triangle is a triangle all of whose sides have lengths that are integers. A rational triangle can be defined as one having all sides with rational length; any such rational triangle can be integrally rescaled (can have all sides multiplied by the same integer, namely a common multiple of their denominators) to obtain an integer triangle, so there is no substantive difference between integer triangles and rational triangles in this sense. Note however, that other definitions of the term "rational triangle" also exist: In 1914 Carmichael〔Carmichael, R. D., 1914, ''Diophantine Analysis'', pp.11-13; in R. D. Carmichael, 1959, ''The Theory of Numbers and Diophantine Analysis'', Dover.〕 used the term in the sense that we today use the term Heronian triangle; Somos〔Somos, M., "Rational triangles," http://grail.csuohio.edu/~somos/rattri.html〕 uses it to refer to triangles whose ratios of sides are rational; Conway and Guy 〔Conway, J. H., and Guy, R. K., "The only rational triangle," in ''The Book of Numbers'', 1996, Springer-Verlag, pp.201 and 228-239.〕 define a rational triangle as one with rational sides and rational angles measured in degrees—in which case the only rational triangle is the rational-sided equilateral triangle.
There are various general properties for an integer triangle, given in the first section below. All other sections refer to classes of integer triangles with specific properties.
==General properties for an integer triangle==
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