*Given a positive integer \(m\), the authors exhibit a group with the probability \(1/m\) that two randomly selected elements commute.*

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*The number \(2\) is a quadratic residue mod \(p\) if \(p = 8k + 1\) or \(p = 8k + 7\), but not if \(p = 8k + 3\) or \(p = 8k + 5\). This is proved by a simple counting argument, assuming the...*

*The author uses Newton`s impact method to compute the centripetal force exerted on a particle moving uniformly on a circumference of a noneuclidean circle.*

*The author gives a mapping of the ordered pairs of positive integers onto the positive integers which is immediately recognizable as a bijection.*

*By exploiting the geometry of the cobweb plot, the author provides a simple and elementary derivation of the parameter for the period-three cycle of the logistic map.*

*The result in the title is demonstrated graphically.*