Question

I’ve just started learning Python and have started doing some problems just to help buid my skills however I am pretty stuck on this question.

Make a list containing all positive integers up to 1000 whose squares can be expressed as a sum of two squares, (i,e., integers p for which p^2=m^2+n^2, where m and n are integers greater than 0.)

Hints: There are several approaches. You might find it helpful to have a list of all the square numbers. The in operator might be useful.

Here’s the code that I’ve come up with so far:

    numbers=xrange(1001)
    numbers_squared=[x**2 for x in numbers]
    a=[]

    for x in numbers_squared:
        for b in numbers_squared:
            if (x+b)**.5 <= 1001:
                a.append(x+b)
    print a

The problem I get with this is that Python takes years to do these calculations (I’ve waited about ten minutes and it’s still printing numbers). Any hints on how to solve this would be very appreciated.

p.s. The main point is to use lists. Also hints would be more appreciated than the solution itself.

Thank You!

Answer 1

how about a list comprehension?
calculate for c in range(1,1011)
for b in range (1, c)
for a in range (1, b)

as follows:

x = [(a,b,c) for c in range(1,1001) for b in range(1, c) for a in range(1,b) if a**2+b**2==c**2]
print x 

I have timed this and it takes 46 seconds to complete on my computer