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Discrete Math question

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Homework Statement



Define the relation a I b ( a divides b) between integers a and b and then define the greatest common divisor, gcd ( a,b), and the lowest common multiple, lcm ( a,b) Is there any number for m for which you have n I m ( n divides by m) for every n.


I just found this one and I have no clue how to do it. It seems difficult to me. Can somebody please explain it to me?
 

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  • #2
HallsofIvy
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You are asked to find an integer that will evenly divide into every integer. First, in order that m divide n evenly, m cannot be bigger than n (in absolute value)! What is the smallest possible absolute value for an integer? What integers have that absolute value? Will they divide into every integer?
 
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You are asked to find an integer that will evenly divide into every integer. First, in order that m divide n evenly, m cannot be bigger than n (in absolute value)! What is the smallest possible absolute value for an integer? What integers have that absolute value? Will they divide into every integer?
I don't know. I suppose that would be 1?
 
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HallsofIvy
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I asked three questions (that I hoped would lead you to the answer). Which was that to answer?
 
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LCKurtz
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Homework Statement



Define the relation a I b ( a divides b) between integers a and b and then define the greatest common divisor, gcd ( a,b), and the lowest common multiple, lcm ( a,b) Is there any number for m for which you have n I m ( n divides by m) for every n.


I just found this one and I have no clue how to do it. It seems difficult to me. Can somebody please explain it to me?
You are asked to find an integer that will evenly divide into every integer...

That may be what he intended to ask, but it isn't what he actually asked, to which the answer is no.

[Edit] Woops. I was thinking natural numbers. Still, it isn't what he asked.
 
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That this integer would be one. If not, no idea.
 
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I'm pretty sure I can find an [tex]n\in\mathbb{Z}[/tex] such that [tex]|n| < 1[/tex].
 

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