Algebra Etc.

Every octagonal number is a difference of two squares youtu.be/CJ3mHDHOIOY

All consistent axiomatic formulations of number theory include undecideable propositions. -- Kurt Gödel

Detailed exploration of a field with nine elements johndcook.com/blog/2022/09/2…

The awkward middle child of algebra johndcook.com/blog/2021/12/0…

'Perfect numbers like perfect men are very rare.' -- Rene Descartes

Every commutative monoid can be extended to a group. -- Grothendieck

There are 17 wallpaper groups.

You can hide a cryptographic key in the order of a deck of cards. How big a deck would you need to store various sizes of keys? johndcook.com/blog/2026/07/2…

The order of a finite field is a prime power, but the characteristic must be a prime.

Python has a built-in method to display floats in hex but not in binary. How to use the former to accomplish the latter. x.com/CompSciFact/st…

A ring R is Noetherian if every ideal of R is finitely generated.

New post: Roots of permutations johndcook.com/blog/2026/07/2…

Excel column labels are not base 26 numbers; they're bijective base 26 numbers. Explanation here: johndcook.com/blog/2026/07/2…

Exact sequences johndcook.com/blog/2021/12/0…

The characteristic of a field is either 0 or a prime.

Every natural number is the sum of at most three triangular numbers. -- Gauss

In the category of rings, an epimorphism is not necessarily surjective. Unlike sets and groups.

Decibels are logs to a different base johndcook.com/blog/2021/05/1…

Today’s exponential sum

Given an m by n chess board, there is a knight's tour for the board if m and n are both at least 5.