dis2@houxm.UUCP (A.NESTOR) (08/21/84)
The mininal M such that:
A: M mod[i] = i-1 for i=2 to n
is sought.
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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
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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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