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Show that for all integers n>2, n does not divide n^2+2

  1. May 5, 2013 #1
    1. The problem statement, all variables and given/known data
    Show that for all integers n>2, n does not divide n^2+2.

    2. The attempt at a solution
    I believe this solution can be solved by induction, I just don't know how to phrase it recursively.

    For all n>2, n^2+2 mod n ≠ 0

    Base case n=3
    3^2 + 2 =11
    11 mod 3 = 2 ≠ 0.

    Show that
    (n-1)^2 +2 mod n-1 ≠ 0
     
  2. jcsd
  3. May 6, 2013 #2

    Office_Shredder

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    I don't think induction is the right way to do this. n divides n2, can you use that in this problem?
     
  4. May 6, 2013 #3
    I can use that, but I'm not sure how it would be done. Intuitively it makes sense, but is there an axiom that I could use that proves this?
     
  5. May 6, 2013 #4

    HallsofIvy

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    Suppose n does divide n2+ 2. Then there exist integer m such that mn= n2+ 2. Now divide both sides by n.
     
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