Orders of consecutive elements does not exceed floor(sqrt(p))
For some prime p, let m = ord_{p}(2) be the multiplicative order of 2 mod p, and m_{2} = ord_{p}(3) be the order of 3 mod p. Let L be the least common multiple of m and m_{2} (L = lcm(m,m_{2})).
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 ≠ b^{i} for some i > 2 or vice versa) are there finitely many primes p such that:
L > floor(sqrt(p))
where
L = lcm(m,m_{2})
m = ord_{p}(a) and m_{2} = ord_{p}(b) ?
Last fiddled with by carpetpool on 20200312 at 02:53
