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Homework Help: Divisors of a number

  1. Apr 8, 2010 #1
    1. The problem statement, all variables and given/known data
    let N= (7^n1)(9^n2)(11^n1)
    if n1 is even,then the total number of divisors of the form of 4k+1 must be divisible by???

    correct answer is n2+1

    3. The attempt at a solution
    total number of divisors = (n1+1)(n2+1)(n1+1)
    Last edited: Apr 9, 2010
  2. jcsd
  3. Apr 9, 2010 #2
    can anybody plz help me uot in this question????
  4. Apr 9, 2010 #3
    can anybody plz help me out in this question????
  5. Apr 9, 2010 #4
    Hm... I don't have the solution, but can give some idea: The factor decomposition is funny, using 9 instead of 3. Anyway, put it like 9^n2 (7*11)^n1. Now get numbers of the form 4k+1: 1, 5, 9, 13, 17, 21, 25... 81... So, you see: powers of 9 are of the form 4k+1. You have to prove that no number of that form can be a multiple of 7 or 11.
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