outer Soddy circle of any right triangle is equal to its semiperimeter. The outer Soddy center is located at , where is a rectangle, the right triangle and its hypotenuse. Only two sides of a primitive Pythagorean triple can be simultaneously prime because by Euclid's formula for generating a primitive Pythagorean triple, one of the legs must be composite and even. However, only one side can be an integer of perfect power because if two sides were integers of perfect powers with equal exponent it would contradict the fact that there are no integer solutions to the Diophantine equation , with , and being pairwise coprime. There are no Pythagorean triangles in which the hypotenuse and one leg are the legs of another Pythagorean triangle; this is one of the equivalent forms of Fermat's right triangle theorem. Each primitive Pythagorean triangle has a ratio of area, , to squared semiperimeter, , that is unique to itself and is given by No primitive Pythagorean triangle has an integer altitude from the hypotenuse; that is, every primitive Pythagorean triangle is indecomposable. The set of all primitive Pythagorean triples forms a rooted ternary tree in a natural way; see Tree of primitive Pythagorean triples. Neither of the acute angles of a Pythagorean triangle can be a rational number of degrees. (This follows from Niven's theorem.) Special cases In addition, special Pythagorean triples with certain additional properties can be guaranteed to exist: Every integer greater than 2 that is not congruent to 2 mod 4 (in other words, every integer greater than 2 which is not of the form ) is part of a primitive Pythagorean triple. (If the integer has the form , one may take and in Euclid's formula; if the integer is , one may take and .) Every integer greater than 2 is part of a primitive or non-primitive Pythagorean triple. For example, the integers 6, 10, 14, and 18 are not part of primitive triples, but are part of the non-primitive triples , and . There exist infinitely many Pythagorean triples in which the hypotenuse and the longest leg differ by exactly one. Such triples are necessarily primitive and have the form . This results from Euclid's formula by remarking that the condition implies that the triple is primitive and must verify . This implies , and thus . The above form of the triples results thus of substituting