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id	title	challengeType	forumTopicId	dashedName
5900f3f71000cf542c50ff0a	Problem 139: Pythagorean tiles	5	301767	problem-139-pythagorean-tiles

--description--

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.

two 5 x 5 squares: one with four 3x4x5 triangles placed to create 1x1 hole in the middle; second with twenty-five 1x1 squares

However, if (5, 12, 13) triangles were used, the hole would measure 7 by 7. These 7 by 7 squares 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 occur?

--hints--

pythagoreanTiles() should return 10057761.

assert.strictEqual(pythagoreanTiles(), 10057761);

--seed--

--seed-contents--

function pythagoreanTiles() {

  return true;
}

pythagoreanTiles();

--solutions--

// solution required

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