a) Write a Python function PrimPyth(n) which returns a list of primitive Pythagorean triples where (x,y,z) where 0 < x < y < z < n . For example, PrimPyth(6) should return [(3,4,5)]. Hint: In this project we represent triples as tuples (x,y,z) not as lists [x,y,z]. The two data-types behave similarly in many ways. Do not write a triply nested loop which searches through all triples (x,y,z) as this will take n^3 steps! Instead, use the fact (proved by Euclid) that every primitive Pythagorean triple arises as (m^2 - n^2, 2mn, m^2 +n^2). where are coprime integers which are not both odd. (Of course the first two entries may be swapped.)

a) Write a Python function PrimPyth(n) which returns a list of primitive Pythagorean triples where (x,y,z) where 0 < x < y < z < n . For example, PrimPyth(6) should return [(3,4,5)]. Hint: In this project we represent triples as tuples (x,y,z) not as lists [x,y,z]. The two data-types behave similarly in many ways. Do not write a triply nested loop which searches through all triples (x,y,z) as this will take n^3 steps! Instead, use the fact (proved by Euclid) that every primitive Pythagorean triple arises as (m^2 - n^2, 2mn, m^2 +n^2). where are coprime integers which are not both odd. (Of course the first two entries may be swapped.)