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7-adic distance in Q7

  1. Nov 19, 2013 #1
    1. The problem statement, all variables and given/known data
    Find the 7-adic distance between -1/3 and the square root of 305 in Q7

    2. The attempt at a solution
    My solution is write the 7-adic expansion of -1/3 and square root of 305

    the 7-adic expansion of -1/3 := 2 +2*7+2*(7^2)+.... =2.2222222(index 7)

    the 7-adic expansion of square root of 305:= 2.22345....(index7) or 5.4432.... this is one representation of root of 305 but there is another representation of 7-adic expansion

    Hence they have the same 7-adic expansion . therefore the distance is 0 in Q7?

    Is my attemption right? ( i am not sure whether i caculated these two 7-adic expansion in a right way)
     
    Last edited: Nov 19, 2013
  2. jcsd
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