The inquisitive reader might ask the following: "Can we set [x]x equal to any integer and always find a solution?" Or, "Are there integers such that our equation would not yield a solution?" Teachers can use this question to have students explore patterns, generate conjectures, and support their reasoning with explanations and proofs. I explore the question using techniques from algebra and number theory and make a surprising connection to a family of numbers studied since the time of Aristotle.
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