Definition:Lucas-Carmichael Number/Mistake
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Source Work
1997: David Wells: Curious and Interesting Numbers (2nd ed.):
- The Dictionary
- $399$
Mistake
- The smallest Lucas-Carmichael number $n$, such that if $p$ divides $n$, then $p + 1$ divides $n + 1$.
It also needs to be stated that:
- $n$ is composite, otherwise all primes would trivially be Lucas-Carmichael numbers
- $n$ is odd and square-free, in order to eliminate several other classes of integer for example, cubes of primes: $p^3 + 1 = \left({p + 1}\right) \left({p^2 - p + 1}\right)$.
Sources
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $399$