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Browse Classroom Capsules and Notes

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Displaying 31 - 40 of 133

Primality testing via repeated differentiation of certain functions is the topic of this paper.
The author discusses the distribution of solutions to a polynomial congruence as the modulus varies.

The authors discuss the existence of functions from the nonnegative reals to the nonnegative reals that satisfy the functional equation underlying Candido`s identity.

The author gives geometrical proofs of a number of identities for the Fibonacci numbers.

The author uses the golden matrix ring \(Z(A)\) generated by \(A= \left[ \begin{array}{cccc} 0 & 1 \\ 1 & 1 \end{array} \right] \) to prove certain identities involving Fibonacci...

Many calculations in number theory have different rules for different residue class mod an integer \(r\). The author shows how to combine these cases using a single amalgamated formula....

Golomb's theorem on \(x/\pi(x)\) about prime number distribution is generalized and has a new proof.

This article gives an explanation why the solution to a number partitioning problem would be \(3\). The answer is that \(3\) is close to \(e\).

A combinatorial proof of the sum of the cubes of the first \(n\) integers is presented, by counting edges in complete bipartite graphs.

A sum is visually presented.