Integer Problem

  • Thread starter dgentile
  • Start date
  • #1
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Homework Statement



Prove that 3 divides one of the integers n, n + 2, or n + 4, for any integer n.


Homework Equations





The Attempt at a Solution


Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
Dick
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Try, ok? Any integer n has a remainder of either 0, 1 or 2 when divided by 3. Come on.
 
  • #3
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Okay...so whats the formula for proving that true is my question?

Thanks
 
  • #4
Dick
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Read the forum rules. You are supposed to put something in the "attempt at a solution section". I just gave you a hint. There really is no 'formula'.
 
  • #5
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Let n be any such integer. THen by the division algorithm there exist integers q and r such that

[tex] n=3q+r,[/tex]

[tex]n+2=3q_1+r[/tex]

[tex]n+4=3q_2+r[/tex] [tex]0\leq r<3[/tex]

i.e r=0, 1 or 2

Now, say if r=0, what happens? if r=1, what happens? if r=2 what happens?

P.S. This is what Dick said, i just wanted to make a little bit easier on you.
YOu MUST show your work next time.
 

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