I am a math noobie, so this might have an obvious solution, but I'd be curious if there is a simple (or a complicated) way to split an integer interval of arbitrary size into exactly n, disjoint sequences so that a set union of all the sequences contains every number in the interval.
I figured one way would include numbers where the lowest common denominator would be larger than (or at least as large as) the largest number in the interval but I have gotten a bit lost on a way as my theoretical framework isn't quite solid enough.
Also, I am very sorry if the textual representation of the requirements is a bit vague, but despite my best effors, task of translating that into some kind of notation was drastically beyond my capabilities.