**Definition:** We say that one integer `a`
*divides* a second integer `b`, and write
`a|b`, if there is a third integer `q` such that
`b = aq`.

As is often the case with precise mathematical definitions like
this one, you have to poke around the edges for a while before you
really understand what it's trying to say. Definitions, like fences,
serve both to keep certain things in and other things out. Everyone
who has survived the standard mathematics courses in elementary school
has confronted the rigors of long division,
and consequently is well aware that you can divide anything (except
`0`) into anything else, provided you are willing to suffer
the slings and arrows of quotients and remainders. The thing that is
being fenced out by the present definition of *divides* is
remainders. We won't allow them. Remainders are forbidden. So,
`3` divides `6`, but `3` does not divide
`7`.

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Kevin R. Coombes

Department of Biostatistics

University of Texas M.D.Anderson Cancer Center

1515 Holcombe Blvd., Box 447

Houston, TX 77030