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Proof in dummit and foote

  1. Feb 15, 2010 #1
    In Dummit and Foote on pages 265-266, a proof is given of the Chinese Remainder Theorem. They claim to proceed by induction, but I cannot see where the induction hypothesis is used.

    It seems that they could proved the statement for k=2, and then reduced the statement for k>2 to k=2. Is this induction?

    Thank you for your help.
     
  2. jcsd
  3. Feb 16, 2010 #2
    I don't have a definite answer, but my feeling is that if your proof for values of n greater than 2 is base upon a showing that it is dependent upon the validity of the case for n = 2 then it is a form of induction.
     
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