Pentagon Numbers
Pentagonal numbers are generated by the formula, $P_n=n(3n-1)/2$. The first ten pentagonal numbers are: $$1, 5, 12, 22, 35, 51, 70, 92, 117, 145, \dots$$
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 are pentagonal and $D = |P_k - P_j|$ is minimised; what is the value of $D$?