Algebra Etc.
@AlgebraFact
Tweets about algebra, number theory, and miscellaneous math by @JohnDCook.
Wilson: If p is prime, (p-1)! is congruent to -1 modulo p.
Addition rules for binomial coefficients and four analogous kinds numbers: q-binomial coefficients, Stirling numbers of the 1st and 2nd kinds, and Eulerian numbers. The basis of Pascal's triangle and analogous triangles.
Every rational number can be written as a finite sum of fractions with numerator 1 and unique denominators. So-called Egyptian fractions.
Taylor Series and the Argentine Peso johndcook.com/blog/2025/07/2…
Analogs of binomial coefficients satisfy analogous addition theorems. johndcook.com/blog/2025/07/2…
GFSR random number generators and primitive polynomials mod 2 johndcook.com/blog/2022/11/0…
Annuity and factorial notation johndcook.com/blog/2025/07/2…
A commutative group is called abelian in honor of Niels Henrik Abel.
Overtones and Barbershop Quartets johndcook.com/blog/2025/04/2…
Base58 versus Base85 encoding johndcook.com/blog/2025/07/2…
'A generating function is a clothesline on which we hang up a sequence of numbers for display.' -- H. S. Wilf
Rules for divisibility by any prime johndcook.com/blog/2021/02/1…
Crystallographic restriction theorem en.wikipedia.org/wiki/Crystallo…
How Kronecker product interacts with inverse, pseudoinverse, and transpose
