# Browse Classroom Capsules and Notes

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Displaying 31 - 40 of 133

Two solutions for the classical coconut dividing problem of the five sailors on an island are given.

Study of linear systems whose coefficients are in arithmetic progression or are powers thereof

A proof of Fermat's Little Theorem

The author gives a numerical analogue to partial fractions.

Certain long divisions of two integers generate digits of the Fibonacci series.

Determining the number of theoretic conditions that will guarantee that a linear congruence is a suitable pseudo-random number generator modulo 16.

Finding multiples of a prime in Pascal's triangle visually

Find a fraction with a decimal expansion matching a specified sequence.

Proof that the square root of a non-square integer is irrational, extended to $n$th roots.

Builds on Nagura's theorem saying that there exists at least one prime between $n$ and $6n/5$ if $n>24$