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Browse Classroom Capsules and Notes

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Displaying 31 - 40 of 133

On Dividing Coconuts: A Linear Diophantine Problem

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

Linear Relations Between Powers of Terms in Arithmetic Progression

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

Fermat's Little Theorem from the Multinomial Theorem

A proof of Fermat's Little Theorem

A Numerical Introduction to Partial Fractions

The author gives a numerical analogue to partial fractions.

A Magic Trick from Fibonacci

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

Pseudorandom Number Generators in a Four-Bit Computer System
Determining the number of theoretic conditions that will guarantee that a linear congruence is a suitable pseudo-random number generator modulo 16.
Locating Multiples of Primes in Pascal's Triangle

Finding multiples of a prime in Pascal's triangle visually

A Generalized Magic Trick from Fibonacci: Designer Decimals

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

Irrational Roots of Integers

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

An Upper Bound on the \(n\)th Prime

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

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