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Prove that if and [j] are equivalence classes modulo

  1. Apr 15, 2008 #1
    Prove that if and [j] are equivalence classes modulo

    1. Prove that if and [j] are equivalence classes modulo n such that =[j], then gcd(i,n)=gcd(j,n)

    2. Prove that if gcd(a,b)=1 and if c divides b, then gcd(a,c)=1.

    plz help
     
  2. jcsd
  3. Apr 23, 2008 #2
    the second part is the easiest if c divides b then b=kc for k an integer

    since gcd(a,b)=1 and gcd(a,c)=gcd(a,kb) then gcd(a,c)=1
     
  4. Apr 23, 2008 #3

    HallsofIvy

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    For (1) use the fact that, if i and j are equivalent mod n, then i- j is a multiple of n.
     
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