Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10 5/3/83 based; site houxm.UUCP 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 sdcsvax!decvax!harpo!eagle!mhuxl!houxm!dis2