Problem 44

p44.py

def is_pentagonal(x):
    #Take the inverse function to test whether or not a number is pentagonal
    if (1+(24*x+1)**0.5) % 6 == 0:
        return True
    return False

def compute():
    k = 1
    while True:
        for j in range(1,k): # this ensures that a > b therefore a-b is minimised 
            a = int((k/2)*(3*k-1))
            b = int((j/2)*(3*j-1))
            if is_pentagonal(a+b) == True and is_pentagonal(abs(a-b)) == True: #Once we find given condition we are done
                print(k,j)
                return (abs(a-b))
        k += 1 #Keep increasing till solution is found