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The solution solution def balanced_centrif uge [ n, k] : This problem was inspired by yet another Numberphile video, this time "The gentrifugg Problem" that you can watch to get an idea what this problem is about, especially since the lovely Dr. Krieger seems a Far better lecturer than this grumpy instructor in most ways that matter. (Despite the chemical inspiration behind this problem, its solulion is not an overly alkaline pH balance.} Those who read faster than they listen can alternatively consult the blog post "We Problem" by Matt Baker. A centrifuge has n identical slots arranged in a rotaling circle. For safe operation of this fast spinning machine, the identical test tubes must be placed on these slots so that their mutual center of gravity lies exactly on the center of the centrifuge. This turns out to be possible for 1: test tubes precisely when both quantities k and 11-]: can somehow be expressed as sums of prime factors of n. For example. when )1 equals 6 so that its prime factors are 2 and 3, it is possible to load the centrifuge safely with 2, 3, 4 or 6 test tubes. [When 1: equals n, the quantity nk equals zero that is always expressible as the empty sum. regardless of the prime factors of 11.} However, there is no way to safely balance one or ve test tubes into six slots; even though 5 = 2 + 3, there is no way to counterbalance the empty slot without making the entire machine wobble dangerously. (Nope, one is still not a prime number, and therefore not a prime factor eithen} This function does not actually need to construct the balanced conguration of test tubes, but simply determine whether some balanced conguration exists at all