Carmichael numbers

In number theory, a Carmichael number is a composite number ${\displaystyle n}$ which satisfies the modular arithmetic congruence relation:

for all integers ${\displaystyle b}$ which are relatively prime to ${\displaystyle n}$. They are named for Robert Carmichael. The Carmichael numbers are the subset K₁ of the Knödel numbers.

Equivalently, a Carmichael number is a composite number ${\displaystyle n}$ for which

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