What Is Special about the Divisors of 24?
نویسنده
چکیده
The divisors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. To pique the reader’s interest and curiosity let us pose the following riddle: what is an interesting number theoretic characterisation of the divisors of 24 amongst all positive integers? There are probably several characterisations of these numbers. In this paper I will provide one characterisation in terms of modular multiplication tables. This idea evolved interestingly from a question raised by my student Elliott in the elementary number theory class. Shortly after introducing the new world of Zn, I asked my students to write down the multiplication tables for Z2,Z3, and Z4. I then showed them the multiplication table for Z8 on the screen (generated by MAPLE) with the intention of drawing their attention to some differences between tables for prime and composite moduli.
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