I'll call it the "Wheel Lug Lemma" for now. If there are a pair of integers p & q such that the Greatest Common Denominator is 1, and there is some number s that is product of p and an increasing whole number n, then the remainder of the division of s by q will cycle through all values of from 0 up to, but not including q until n is equal to q at which time the remainder is 0, with the cycle repeating again in the same order. The idea is if there is a wheel with p # of lug nuts, and the lug nuts are tightened in the order skipping q # of lug nuts to tighten the next nut, then eventually every lug nut will get tightened before encountering one that has already been tightened. For example, typically a wheel has q = 5 lug nuts, and it is recommended that they be tightened in a star pattern, so that they are done in the order of 0, 2, 4, 1, 3, and thus with p = 2 skipping. 0 % 5 = 0 2 % 5 = 2 4 % 5 = 4 6 % 5 = 1 8 % 5 = 3 → all possible remainder have been cycled through 10 % 5 = 0 → the cycle repeats I figure that someone must have recognized this and wrote it up as a lemma somewhere.