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N is prime if and only if

  1. Jul 6, 2014 #1
    An integer is prime if, and only if, n > 1 and for all positive integers r and s, if
    n = (r)(s), then r > 1 or s > 1.

    it should be if n = rs, then r great than or equal 1 or s greater than or equal 1

    correct?
     
  2. jcsd
  3. Jul 6, 2014 #2

    verty

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    Homework Helper

    What you want to say is that no factor is between 1 and n. If either is 1, it works.
     
  4. Jul 6, 2014 #3

    HallsofIvy

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    What? No! if 6= (r)(s) then either r= 3 and s= 2 or r= 2 and s= 3 or r= 1 and s= 6 or r= 6 and r= 1. "If n= (r)(s), then r> 1 or s> 1" is true for all positive integers except 1.

    This is now true for all positive integers. What is true for prime numbers only is "If n= (r)(s) then r= 1 or s= 1."
     
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