Integers and FractionsDate: 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/ |
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