Algebra Etc.@AlgebraFact

Tweets about algebra, number theory, and miscellaneous math by @JohnDCook.

JohnDCook.com
Joined January 2010
2,030 Photos and videos
For each prime p and positive integer n, there is a unique field of order p^n.
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Every field is an integral domain. Every finite integral domain is a field.
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A symmetric matrix is positive definite iff the determinant of every upper-left submatrix is positive.
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Limits on Venn diagrams johndcook.com/blog/2024/09/2…

Limitations on Venn diagrams

Why do Venn diagrams almost always show the intersections of three sets and not more? Can Venn diagrams be generalized to show all intersections of more sets? That depends on the rules you give...

johndcook.com
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If a finite group G has k elements and p^n is the highest power of a prime p dividing k, then G has a subgroup of order p^n. -- Sylow
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Math documentaries cosmolearning.org/mathematic… via @MathUpdate
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Binomial Coefficient Coincidences johncarlosbaez.wordpress.com…

Binomial Coefficient Coincidences

These seven equations between binomial coefficients are ‘coincidences’: they aren’t among the four known infinite families. De Weger conjectured that there are no more such coinci…

johncarlosbaez.wordpress.com
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The Fermat numbers F_0 thru F_4 are prime. Euler found that F_5 is composite.
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Solving a chess puzzle with Claude and Z3/Python Place all the pieces—king, queen, two bishops, two knights, and two rooks—on a 6 × 5 chessboard, with the requirement that the two bishops be on opposite colored squares and no piece is attacking another. johndcook.com/blog/2026/06/2…
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Fermat numbers have the form 2^{2^m} + 1.
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New post: Nathaniel Bowditch johndcook.com/blog/2026/09/2…
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The Star Trek Lemma johndcook.com/blog/2026/06/2…
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VIN (Vehicle Identification Number) check sums johndcook.com/blog/2019/09/1…

Vehicle Identification Number (VIN) check sum

A VIN (vehicle identification number) is a 17 character code associated to a motor vehicle. In North America, one of these 17 digits is a check sum.

johndcook.com
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A field is a ring in which non-zero elements form an abelian group under multiplication.
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The sum of the reciprocals of the primes diverges.
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A matrix A is skew-Hermitian if A^* = -A.
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Equation of a conic section through five points johndcook.com/blog/2023/06/1…

Equation of an ellipse or hyperbola through five points

Find the equation of an ellipse or hyperbola through five points. With Python code.

johndcook.com
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Enumerating trees and circles johndcook.com/blog/2026/08/0…
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The sum of Hermitian matrices is Hermitian.
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A matrix A is Hermitian if it is self-adjoint, i.e. A^* = A.
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