OFFSET
1,1
COMMENTS
Right integer triangles have integer areas: see A070143.
LINKS
Eric Weisstein's World of Mathematics, Heronian Triangle.
Eric Weisstein's World of Mathematics, Right Triangle.
Reinhard Zumkeller, Integer-sided triangles
EXAMPLE
MATHEMATICA
m = 500 (* max perimeter *);
sides[per_] := Select[Reverse /@ IntegerPartitions[per, {3}, Range[ Ceiling[per/2]]], #[[1]] < per/2 && #[[2]] < per/2 && #[[3]] < per/2 &];
triangles = DeleteCases[Table[sides[per], {per, 3, m}], {}] // Flatten[#, 1] & // SortBy[Total[#] m^3 + #[[1]] m^2 + #[[2]] m + #[[1]] &];
Position[triangles, {a_, b_, c_} /; GCD[a, b, c] == 1 && a^2 + b^2 - c^2 == 0] // Flatten (* Jean-François Alcover, Oct 04 2021 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, May 05 2002
EXTENSIONS
More terms from Jean-François Alcover, Oct 04 2021
STATUS
approved