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Congruence Properties

Proposition: Let a and a' be in the same residue class and also b and b' be in the same residue class. The result of any integer operation involving a and b is in the same residue class as if the operation were performed with a' and b' instead:

forall m in Z>0, a in Z, a' in Z, b in Z, b' in Z:
   [a]m = [a']m /\  [b]m = [b']m =>
      [a+b]m = [a'+b']m /\ 
      [-a]m = [-a']m /\ 
      [a*b]m = [a'*b']m.

Author: Wolfgang Schreiner
Last Modification: January 12, 2000

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