561 is the smallest Carmichael number in the ring of integers. However it is only a pseudoprime in the ring of Gaussian integers. We can use pari to find the bases to which 561 is a pseudoprime. I found it is pseudoprime to bases 12 + i, 22 +i, 34 + i and 56 + i. Needless to say it is a pseudoprime to other bases too. More on this later.

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