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In mathematics, a Lucas–Carmichael number is a positive composite integer n such that

The first condition resembles the Korselt's criterion for Carmichael numbers, where -1 is replaced with +1. The second condition eliminates from consideration some trivial cases like cubes of prime numbers, such as 8 or 27, which otherwise would be Lucas–Carmichael numbers is always divisible by n + 1].

They are named after Édouard Lucas and Robert Carmichael.

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