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Proof for n

  1. Jan 27, 2009 #1
    Suppose n=ab, show that a^2<=n or b^2<=n.
     
  2. jcsd
  3. Jan 27, 2009 #2

    CRGreathouse

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    Start with trichotomy: a < b, a = b, or a > b. It's pretty simple.
     
  4. Jan 27, 2009 #3
    I'm fairly new to proofs, so can you please check if this is correct.

    if a=b, n=a^2 or b^2=n
    if a>b, a^2>ab, a^2>n
    if b>a, b^2>ab, b^2>n
     
  5. Jan 27, 2009 #4

    CRGreathouse

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    What you write is correct, though for the last two you should really use the opposite variable (and reverse signs) because you're trying to show that something's smaller, not bigger.
     
  6. Jan 27, 2009 #5
    Try multiplying a > b by b instead of by a.
     
  7. Jan 27, 2009 #6
    so it should be like this then:

    if a>b, ba>b^2, n>b^2
    if b>a, ab>a^2, n>a^2
     
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