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Homework Help: Perfect and amicable numbers

  1. Feb 2, 2010 #1
    1. The problem statement, all variables and given/known data

    Show that if p is a prime, then p^n is deficient.

    2. Relevant equations

    3. The attempt at a solution

    I have no idea where to start.
  2. jcsd
  3. Feb 2, 2010 #2
    You could start with the definition of a deficient number.
    If p is prime, it's only divisors are 1 and p and thus, the sum of it's divisors is p+1.
    What are the divisors of pn?
  4. Feb 2, 2010 #3
    would be P^n +P^1+P^0 correct?
  5. Feb 3, 2010 #4
    If p is prime, then it's only divisors are 1 and p. The divisors of pn are also 1 and p, which sum to p+1. Apply this to the criteria of a deficient number.
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