If gcd(a,b) = 1 then b divides a^(n1)  1, and a divides b^(m1)  1, so
znorder(Mod(b,a)) divides n1 and znorder(Mod(a,b)) divides m1.
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 b1, assuming a < b.
If m <> n the equation
a^{n}  b^{m} = 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.
