
 Modular Arithmetic, Fermat Theorem, Carmichael Numbers  Numericana 
  Note that, when the moduli are not pairwise coprime, some potential sets of "remainders" are ruled out: For example, no integer can leave a remainder of 2 when divided by 6 and a remainder of 3 when divided by 4... 
  Modulo 10, for example, the reciprocal of 7 is 3, whereas 1 and 9 are their own reciprocals (the residues 0,2,4,5,6,8 are not coprime to 10 and have therefore no reciprocal modulo 10). 
  There are 72 residues coprime to 91 (72 is the Euler totient of 91). 
 home.att.net /~numericana/answer/modular.htm (3088 words) 
