Special right triangle than 256: Isosceles right-angled triangles cannot have sides with integer values, because the ratio of the hypotenuse to either other side is , but cannot be expressed as a ratio of two integers. However, infinitely many "almost-isosceles" right triangles do exist. These are right-angled triangles with integral sides for which the lengths of the non-hypotenuse edges differ by one. Such almost-isosceles right-angled triangles can be obtained recursively, "a" is length of hypotenuse, "n" = 1, 2, 3, ... Equivalently, where {"x", "y"} are the solutions to the Pell equation , with the hypotenuse "y" being the odd terms of the
Fermat's right triangle theorem Fermat's right triangle theorem Fermat's right triangle theorem is a non-existence proof in number theory, the only complete proof left by Pierre de Fermat. It has several equivalent formulations: An immediate consequence of the last of these formulations is that Fermat's last theorem is true for the exponent formula_3 and hence for any multiple of 4. In 1225, Fibonacci was challenged to find a construction for triples of square numbers that are equally spaced from each other, forming an arithmetic progression, and for the spacing between these numbers, which he called a congruum. One way of describing Fibonacci's solution is