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).