Pentagon numbers
Problem 44
Pentagonal numbers are generated by the formula, Pn=n(3nāˆ’1)/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 āˆ’ 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 āˆ’ Pj| is minimised; what is the value of D?