Integer triangle rational formula_14 where formula_15 reduces the generated Heronian triangle to its primitive and formula_16 scales up this primitive to the required size. A Pythagorean triangle is right angled and Heronian. Its three integer sides are known as a Pythagorean triple or Pythagorean triplet or Pythagorean triad. All Pythagorean triples formula_17 with hypotenuse formula_18 which are primitive (the sides having no common factor) can be generated by where "m" and "n" are coprime integers and one of them is even with "m" > "n". Every even number greater than 2 can be the leg of a Pythagorean triangle (not necessarily primitive)
Fermat's right triangle theorem and the other is odd. Therefore, both formula_39 and formula_40 are even, one of which is divisible by 4. From these two numbers Fermat derives two more numbers formula_41 and formula_42, one of which is even by the previous sentence. Because formula_43 is a square, formula_44 and formula_45 are the legs of another primitive Pythagorean triangle whose area formula_46. Since formula_27 is itself a square and since formula_48 is even, formula_49 is a square. Thus, any Pythagorean triangle with square area leads to a smaller Pythagorean triangle with square area, completing the proof. Fermat's right triangle theorem Fermat's right triangle