Solutions to the equation [x]x = n

• Autores: Lee Melvin Peralta, Daniel Ness (ed. lit.), Nick Wasserman (ed. lit.), Benjamin Dickman
• Localización: Mathematics teacher, ISSN-e 2330-0582, ISSN 0025-5769, Vol. 111, Nº 2, 2017, págs. 150-154
• Idioma: inglés
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• Resumen

  • 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.