A Carmichael number is a composite number n that satisfies, for every integer b, the same congruence relation that Fermat's Little Theorem guarantees for a prime modulus: b raised to the n is congruent to b modulo n. Carmichael numbers are infinite in number and constitute the comparatively rare instances where the strict converse of Fermat's Little Theorem fails, which is why the theorem cannot be used as an absolute test of primality. They form the subset K1 of the Knodel numbers. The numbers are named after the American mathematician Robert Carmichael by Nicolaas Beeger in 1950; Oystein Ore had earlier referred to them in 1948 as numbers with the Fermat property, or F numbers for short.
Facts
Sources
1. Wikipedia: Carmichael number
Lead paragraph
In number theory, a Carmichael number is a composite number n which in modular arithmetic satisfies the congruence relation: b^n ≡ b (mod n) for all integers b.
History section
In 1910, Carmichael himself also published the smallest such number, 561, and the numbers were later named after him.
View the SourceReader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.