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Integers and Fractions


Date: 03/23/2002 at 19:14:37
From: Filgi K Mathew
Subject: Divisor

1. Give an example of a positive integers p, a, b where p/ab and not 
p/a and not p/b.

2. Let m, n, and c be integers. Show that if c/m then c/mn.


Date: 03/23/2002 at 19:18:40
From: Doctor Paul
Subject: Re: Divisor

1. Pick p = 4, a = 2, b = 6

   Then certainly 4|12 but plainly 4 does not divide 2 (since 2 < 4) 
   and 4 does not divide 6.

2. c|m means that there exists an integer k such that c*k = m.

   Then c*k*n = m*n.

   To show that c|(m*n), we want to exhibit an integer p such that
   c*p = m*n

   Plainly, letting p = k*n will do the job.

I hope this helps.  Please write back if you'd like to talk about this 
some more.

- Doctor Paul, The Math Forum
  http://mathforum.org/dr.math/   
    
Associated Topics:
High School Number Theory

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