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Old 2006-01-04, 06:58   #5
cheesehead
 
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"Richard B. Woods"
Aug 2002
Wisconsin USA

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Quote:
Originally Posted by devarajkandadai
5 is the minimum universal exponent (w.r.t base 2) i.e.

(2^5) - 1 =31 and 5 is the minimum exp such that 2^n - 1 is congruent to
zero (mod 31).
But why is 5 the minimum universal exponent with respect to base 2, and not 3 or 2 or even 1, for example? After all, 3 or 2 (or 1) satisfies the same statement you give for 5:

(2^3) - 1 =7 and 3 is the minimum (positive) exponent such that 2^n - 1 is congruent to zero (mod 7).

(2^2) - 1 =3 and 2 is the minimum (positive) exponent such that 2^n - 1 is congruent to zero (mod 3).
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