Pentagonal numbers are generated by the formula, Pn=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 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? |
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