code: def solve():
      """
      Pentagonal numbers are generated by the formula, P_n=n(3n-1)/2. The first ten pentagonal numbers are:
  
      1, 5, 12, 22, 35, 51, 70, 92, 117, 145, ...
  
      It can be seen that P_4 + P_7 = 22 + 70 = 92 = P_8. However, their difference, 70 - 22 = 48, is not pentagonal.
  
      Find the pair of pentagonal numbers, P_j and P_k, for which their sum and difference is pentagonal and D = |P_k - P_j| is minimised; what is the value of D?
      """
  
      MAX = 2000
      pent = [n * (3 * n - 1) / 2 for n in range(1, 2 * MAX)]
      pdic = dict.fromkeys(pent)
  
      def main2():
          for j in range(0, MAX):
              for k in range(j + 1, 2 * MAX - 1):
                  p_j = pent[j]
                  p_k = pent[k]
                  p_sum = p_j + p_k
                  p_diff = p_k - p_j
                  if p_sum in pdic and p_diff in pdic:
                      return p_diff
  
      return main2()
  
label_desc: Use image node_id 1 for calling a global function with example usage: solve() and returns: main2, p_diff