218 Pythagorean triples
7.Give an example of a primitive Pythagorean triangle in which the
oddleg is a square. triangle to be a square?8.Find the shortest perimeter common to two different primitive Pythagorean
triangles.9.Find an integer-sided right angled triangle with sidesx^2 − 1 ,y^2 − 1
z^2 − 1 , wherex,y,zare integers.10.The number ofprimitivePythagorean triangle with a fixed inradius
is always a power of 2.
11.Show that there are an infinite number of Pythagorean triangles
whose hypotenuse is an integer of the form 3333 ··· 3.12.For each natural numbern, how many Pythagorean triangles are
there such that the area isntimes the perimeter? How many of
these are primitive?