Mathematicians wanted to better understand these numbers that so closely resemble the most fundamental objects in number theory, the primes. It turned out that in 1899—a decade before Carmichael’s result—another mathematician, Alwin Korselt, had come up with an equivalent definition. He simply hadn’t known if there were any numbers that fit the bill.
According to Korselt’s criterion, a number N is a Carmichael number if and only if it satisfies three properties. First, it must have more than one prime factor. Second, no prime factor can repeat. And third, for every prime p that divides N, p – 1 also divides N – 1. Consider again the number 561. It’s
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