Egyptian_fraction

import math
import time

n = 11
start = math.ceil(n/4.0)


def run():
    for a in range(start, start + 10000):
        for k in range(1,500000):
            P = a*k
            for j in range(1,10000):
                S = 4.0*P/j - k
                delta2 = S*S-4*P
                if delta2 >= 0:
                    b = (S + math.sqrt(delta2))/2.0
                    c = (S - math.sqrt(delta2))/2.0
                    if b >= start and c >= start and math.floor(b) == b and math.floor(c) == c:
                        if n == (4.0*a*b*c)/(a*b + b*c + c*a):
                            print('a b c are', a,b,c)
                            return a,b,c

print("n = ", n)
start_time = time.time()
run()
print("It takes ", time.time()-start_time)