Sum of two squares in Python ?

You do not need the ranges at all, and certainly do not need to convert them into tuples. They take a ridiculous amount of space, but you only need their current elements, numbers i and j. Also, as the friendly commenter suggested, you can start with sqrt(n) to improve the performance further.

def sum_of_two_squares(n):
    i = 1
    j = int(n ** 1/2)

    while i < j:
        x = i * i + j * j
        if x == n:
            return j, i

        if x < n:
            i += 1
        else:
            j -= 1