data/problems/44.yml
---
:id: 44
:name: Pentagon numbers
:url: https://projecteuler.net/problem=44
:content: |+
Pentagonal numbers are generated by the formula, P<sub><var>n</var></sub>=<var>n</var>(3<var>n</var>−1)/2. The first ten pentagonal numbers are:
1, 5, 12, 22, 35, 51, 70, 92, 117, 145, ...
It can be seen that P<sub>4</sub> + P<sub>7</sub> = 22 + 70 = 92 = P<sub>8</sub>. However, their difference, 70 − 22 = 48, is not pentagonal.
Find the pair of pentagonal numbers, P<sub><var>j</var></sub> and P<sub><var>k</var></sub>, for which their sum and difference are pentagonal and D = |P<sub><var>k</var></sub> − P<sub><var>j</var></sub>| is minimised; what is the value of D?