Algebra Etc. @AlgebraFact
Tweets about algebra, number theory, and miscellaneous math by @JohnDCook. JohnDCook.com Joined January 2010-
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Conway's Little Theorem: A triangle is equilateral if and only if the ratio between the length of any two sides is rational and the ratio between any two angles is also rational.
Every prime number of the form 4n + 1 is the sum of two squares in exactly one way.
Pulling on a thread: How an approximation lead to a series of nine posts. johndcook.com/blog/2026/06/1…
Mentally calculate scientific calculator functions to around two significant figures. johndcook.com/blog/mental-fu…
Let f(n) be the nth Fibonacci number. Then f(mn) is divisible by f(m)f(n) iff gcd(m,n) = 1, 2, or 5.
If m divides n, then b^m - 1 divides b^n - 1 for all b > 1.
A cranky formula for π johndcook.com/blog/2026/06/0…
For positive integer n, f(n) = 2^(2^(n+1)) + 2^(2^n) + 1 has at least n+1 distinct prime factors. cut-the-knot.org/proofs/Infinit…
Mentally testing for divisibility by a sequence of primes johndcook.com/blog/2023/03/0…
252nd Carnival of Mathematics fractalkitty.com/the-252nd-carn…
The pair (p, p+2) are twin primes iff 4((p-1)! + 1) + p = 0 mod p(p+2). -- Clement's theorem
Studying an analysis question led to a combinatorial question: Ratio of partitions to permutations. johndcook.com/blog/2026/06/0…
Let f(n, j) be the number of permutations of a set of n elements with j fixed points. Then f(n, 1) = f(n, 0) - (-1)^n.
Why are Noetherian Rings Special? math3ma.com/blog/why-are-n…
Finding where two conic sections intersect johndcook.com/blog/2022/10/2…
The only Fibonacci numbers that are cubes are 1 and 8.
Random hexagonal fractals Different ways of defining the center of a triangle lead to different images. johndcook.com/blog/2026/04/0…
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