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Problem

A sequence is arithmetic if the numbers increases by a fixed amount. For example, 2, 5, 8, are in an arithmetic sequence with a common difference of 3, and if these numbers represented the side lengths of a cuboid, the volume, V = 258 = 80 units³.

How many cuboids exist for which the volume is less than 100 units³ and the integer side lengths are in an arithmetic sequence?