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Homework Help: Number Theory least divisor of integer is prime number if integer is not prime

  1. Mar 26, 2012 #1
    1. The problem statement, all variables and given/known data
    The question is not really a question from a book but rather a statement that it makes : it says " Obviously the least divisor[excluding 1] of an integer a is prime if a itself is not prime." I kind of believe this statement but I'm having trouble proving the general case

    2. Relevant equations

    3. The attempt at a solution
    when I take a few examples : a =8 , 2 (LD) is prime . a = 10, 2(LD) . a = 9, 3(LD) is prime a =121, 11(LD) is prime. But i'm having trouble generalizing this for all n.
  2. jcsd
  3. Mar 26, 2012 #2
    any non-prime divisor can be further divided.
  4. Mar 26, 2012 #3
    Thank you! I feel stupid but happy I understand now.
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