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Old 2018-12-03, 16:49   #6
Dr Sardonicus
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Feb 2017

2·7·271 Posts

If gcd(a,b) = 1 then b divides a^(n-1) - 1, and a divides b^(m-1) - 1, so

znorder(Mod(b,a)) divides n-1 and znorder(Mod(a,b)) divides m-1.

This might tend to push up the possible values of m and n for a given a and b. (One way to keep at least one of the znorders small is if a divides b-1, assuming a < b.

If m <> n the equation

an - bm = a - b

is curious, in that (1) if m and n are greater than 1, the difference in powers is quite small, and (2) with m and n different, the difference being divisible by a - b is curious.
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