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Path: utzoo!watmath!clyde!burl!ulysses!mhuxl!houxm!dis2
From: dis2@houxm.UUCP (A.NESTOR)
Newsgroups: net.math
Subject: Re:A hard one?
Message-ID: <840@houxm.UUCP>
Date: Tue, 21-Aug-84 12:49:53 EDT
Article-I.D.: houxm.840
Posted: Tue Aug 21 12:49:53 1984
Date-Received: Wed, 22-Aug-84 01:41:56 EDT
Organization: AT&T Bell Labs, Holmdel NJ
Lines: 36


  The mininal M such that:
         A:  M mod[i] = i-1 for i=2 to n
  is sought.
  ---------------------------------------------------------------
  
  1) By the defintion of mod, A implies:
         B:  For all i, i is a divisor of M-(i-1)
             i.e (M+1 -i)/i = k where k is an integer)
   
  2) B implies that:
         C:  For all i, i divides M+1
              i.e (M+1)/i = k where k is an integer
    
  3) By the defintion of the Least Common Multiple(LCM):
         D: M+1 is minimal when it is equal to the LCM of i=2 to n
    
  4) D implies:
          M = (LCM of i = 2 to n) -1
  ---------------------------------------------------------------
   For example:
       n      M
      ___   ______
       2     1
       3     5
       4     11
       5     59
       6     59
       7     419
       8     839
       9     2519
      10     2519
      11     27719
      12     27719
					Creighton Clarke
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