# Problem 139: Pythagorean tiles

![graphic](img139.gif)

Let (a, b, c) represent the three sides of a right angle triangle with
integral length sides. It is possible to place four such triangles
together to form a square with length c. For example, (3, 4, 5)
triangles can be placed together to form a 5 by 5 square with a 1 by 1
hole in the middle and it can be seen that the 5 by 5 square can be
tiled with twenty-five 1 by 1 squares. However, if (5, 12, 13) triangles
were used then the hole would measure 7 by 7 and these could not be used
to tile the 13 by 13 square. Given that the perimeter of the right
triangle is less than one-hundred million, how many Pythagorean
triangles would allow such a tiling to take place?