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?uestionable
Does anyone know if a Carmichael number returns 1 if you use Fermat's Little Theorem on it base 3?
Carmichael numbers are composite numbers that satisfy the conditions of Fermat's Little Theorem in any base. This means that for any base, raised to the power of a Carmichael number, the remainder will always be 1.
Unlike prime numbers, Carmichael numbers are composite, meaning they can be factored into smaller numbers. However, they share a similar property with prime numbers in that they are only divisible by 1 and themselves.
To identify a Carmichael number in a different base, you can use the Fermat primality test. This involves checking if the number satisfies Fermat's Little Theorem in that base. If it does, then it is a Carmichael number.
There are a few known patterns of Carmichael numbers in other bases. For example, in base 2, all Carmichael numbers end in 101. In general, Carmichael numbers tend to have a lot of small prime factors.
Carmichael numbers play a significant role in cryptography, particularly in the RSA algorithm. These numbers are used to generate keys and encrypt messages, making them an essential component of secure communication.