What is special about the divisors of 24?

Details What is special about the divisors of 24? What is special about the divisors of 24?

2011-04-27

arxiv.org/abs/1104.5052v2

Mathematics

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6 pages, fixed some typos and added a few references

Scientific paper

What is an interesting number theoretic or a combinatorial characterization of the divisors of 24 amongst all positive integers? In this paper I will provide one characterization in terms of modular multiplication tables. This idea evolved interestingly from a question raised by a student in my elementary number theory class. I will give the characterization and then provide 5 different proofs using various techniques: Chinese remainder theorem, structure theory of units, Dirichlet's theorem on primes in an arithmetic progression, Bertrand-Chebyshev theorem, and results of Erdos and Ramanujan on the pi(x) function.

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