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From: kp@smu.UUCP
Newsgroups: net.math
Subject: INTERESTING NUMBERS - (nf)
Message-ID: <14100005@smu.UUCP>
Date: Sun, 29-Apr-84 17:31:00 EDT
Article-I.D.: smu.14100005
Posted: Sun Apr 29 17:31:00 1984
Date-Received: Thu, 3-May-84 20:01:09 EDT
Lines: 34
Nf-ID: #N:smu:14100005:000:994
Nf-From: smu!kp    Apr 29 16:31:00 1984

#N:smu:14100005:000:994
smu!kp    Apr 29 16:31:00 1984


       Let us consider "INTERESTING" numbers:
           (let us stick to only positive integers)

   1  : it is the least positive integer; multiplication identity etc...
   2  : it is the oddest prime(the only even prime!)
   3  : first odd prime
   4  : first nontrivial perfect square
   5  : PENTAGON!
   6  : first perfect number ( 6 = 3 + 2 + 1)
   7  : 7 days in a week,7 notes, 7 colors, etc....
   8  : first nontrivial cube
   9  : first composite odd number
          
        etc,    etc,    the list could be continued.


      Can anyone prove that the following are interesting numbers:

          (a) 17    (b) 100   (c) 1729   (d) 127

           In general, using proof by contradiction it can be proved
that all numbers are interesting. Can anyone give a short proof?
           Identify the flaw in such a proof, if any??


                                   - KP -
                               Dept of Comp Sci
                               SMU, Dallas, TX