OFFSET
1,1
COMMENTS
There are no further terms. Note that without the condition "integer-sided" there are other solutions, such as (9/2, 20, 41/2) which has perimeter and area 45. - David Wasserman, Jan 03 2008
REFERENCES
S. Ainley, Mathematical Puzzles, Problem J8 p. 113, G. Bell & Sons Ltd, London (1977).
LINKS
James Grime and Brady Haran, Superhero Triangles, Numberphile video (2020)
EXAMPLE
The areas or perimeters 24, 30, 36, 42, 60 pertain respectively to triangles with sides (6, 8, 10), (5, 12, 13), (9, 10, 17), (7, 15, 20), (6, 25, 29).
MATHEMATICA
m0 = 10 (* = initial max side *); okQ[{x_, y_, z_}] := x <= y <= z && (-x + y + z) (x + y - z) (x - y + z) (x + y + z) == 16 (x + y + z)^2; Clear[f];
f[m_] := f[m] = Select[Tuples[Range[m], 3], okQ]; f[m = m0]; f[m = 2 m]; While[f[m] != f[m/2], m = 2 m]; sides = f[m]; Total /@ sides // Sort (* Jean-François Alcover, Jul 21 2017 *)
CROSSREFS
KEYWORD
fini,full,nonn
AUTHOR
Lekraj Beedassy, Sep 10 2004
STATUS
approved