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Complete residue system Question

  1. Feb 22, 2010 #1
    Hi i am doing self-study of number theory as it looks interesting and enlightening.
    Can someone help because I encounter a problem here..
    Suppose A = {a1,a1,,,,,,,ak} is a complete residue system modulo k. Prove that for each integer n and each nonnegative integer s there exists a congruence of the form
    n ≡ (sum j=0 to s)bj kj ( mod ks+1 )
    where bj[tex]\in[/tex] A for each j .
     
  2. jcsd
  3. Feb 22, 2010 #2

    CRGreathouse

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    a_1 and a_k are relatively prime, so you can use the extended Euclidean algorithm to find constants A and B with Aa_1 + Ba_k = 1. Then take (An)a_1 + (Bn)a_k.
     
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