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Browse Classroom Capsules and Notes

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Displaying 71 - 80 of 133

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.

Integers equaling the sum of the squares of their contiguous parts (a generalization of two-digit numbers which are the sum of the squares of their digits) are discussed, with several examples...

A Smith number is a composite number the sum of whose digits is the sum of all the digits of all its prime factors. The author reviews the history of these numbers, starting with the proof that...
The article discusses prime numbers which remain prime after the permutation of the digits.
This article contains a geometric demonstration of an identity for integers.

The author presents a new Identity for integer functions and their inversion formulas.

The article discusses the reason for studying finite fields.

A simple geometric proof for the formula \(1 + 3 + 5 + \ldots + (2n - 1) + (2n + 1) + (2n - 1) + \ldots + 5 + 3 + 1 = n^2 + (n + 1)^2\)