# Browse Classroom Capsules and Notes

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Displaying 81 - 90 of 133

Certain subsets of the ring of integers mod $n$ with hidden group structure are discussed.

An identity between certain squares and sums of fourth powers is exhibited, which can be used to establish a Fibonacci identity.
The authors investigate how to partition the integers into three arithmetic progressions.

The authors provide a proof, accessible to beginning number theory students, of Chebychevs upper bound on the number of primes no greater than n.

After a brief historical discussion of the aliquot parts of an integer the authors use elementary arguments to prove a theorem about the sums of its principal divisors.

The author discusses an alternate way of developing Binets formula. See also a follow-up letter from Art Benjamin in Mathematics Magazine, Volume 78, No. 2, page 97.

The authors consider expansions of rationals to any base $b$, with special attention to inverses of Wieferich primes.

The author discusses the development of formulas for questions about primes.
Techniques for the construction of Smith numbers are presented.

The squares are summed visually.