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Old 2020-03-12, 02:50   #1
carpetpool
 
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"Sam"
Nov 2016

22·83 Posts
Post Orders of consecutive elements does not exceed floor(sqrt(p))

For some prime p, let m = ordp(2) be the multiplicative order of 2 mod p, and m2 = ordp(3) be the order of 3 mod p. Let L be the least common multiple of m and m2 (L = lcm(m,m2)).

Does a prime p exist such that L < sqrt(p) or simply floor(sqrt(p)) ?

(There is no such prime below 10^9)

The question in general is, for integers (a,b) (a ≠ bi for some i > 2 or vice versa) are there finitely many primes p such that:

L > floor(sqrt(p))

where
L = lcm(m,m2)
m = ordp(a) and m2 = ordp(b) ?

Last fiddled with by carpetpool on 2020-03-12 at 02:53
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