## Pentagon numbers

### Problem 44

Published on Friday, 23rd May 2003, 06:00 pm; Solved by 24736

Pentagonal numbers are generated by the formula, Pn=n(3n1)/2. The first ten pentagonal numbers are:

1, 5, 12, 22, 35, 51, 70, 92, 117, 145, ...

It can be seen that P4 + P7 = 22 + 70 = 92 = P8. However, their difference, 70 22 = 48, is not pentagonal.

Find the pair of pentagonal numbers, Pj and Pk, for which their sum and difference are pentagonal and D = |Pk Pj| is minimised; what is the value of D?