Solution Exercise 69: python algorithm which determines the list of tuples of integers satisfying certain condition

Exercise 69

Write a Python algorithm which determines for a given integer n the list of tuples of integers (p, q) satisfying:

p2 + q2 = n

Solution

#coding: utf-8
def listTuple (n):
    # initialization of the list of couples (p, q)
    tupleList = []

    # iterate over the set of tuples (p, q) such that p <= n and q <= n
    for p in range (0, n + 1):
        for q in range (0, n + 1):
            if p**2 + q**2 == n:
                tupleList.append ((p, q))
    return tupleList
# Example n = 1000
print (listTuple (1000)) #output:  [(10, 30), (18, 26), (26, 18), (30, 10)]