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

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  • #1
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Homework Statement


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
 

Answers and Replies

  • #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?
 
  • #3
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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?
 
  • #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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