text: 
  # -*- coding: utf-8 -*-
  '''
      File name: code\four_representations_using_squares\sol_229.py
      Author: Vaidic Joshi
      Date created: Oct 20, 2018
      Python Version: 3.x
  '''
  
  # Solution to Project Euler Problem #229 :: Four Representations using Squares
  # 
  # For more information see:
  # https://projecteuler.net/problem=229
  
  # Problem Statement 
  '''
  Consider the number 3600. It is very special, because
  
  3600 = 482 +     362
  3600 = 202 + 2×402
  3600 = 302 + 3×302
  3600 = 452 + 7×152
  
  Similarly, we find that 88201 = 992 + 2802 = 2872 + 2×542 = 2832 + 3×522 = 1972 + 7×842.
  
  In 1747, Euler proved which numbers are representable as a sum of two squares.
  We are interested in the numbers n which admit representations of all of the following four types:
  
  n = a12 +   b12n = a22 + 2 b22n = a32 + 3 b32n = a72 + 7 b72,
  
  where the ak and bk are positive integers.
  
  There are 75373 such numbers that do not exceed 107.
  
  How many such numbers are there that do not exceed 2×109?
  '''
  
  # Solution 
  
  # Solution Approach 
  '''
  '''
  