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Carmichal number 561

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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,
33  +  i  and  44  +  i.  Needless  to  say  it is  a
pseudoprime to  other  bases  too. More  on  this later.