Quote:
Originally Posted by mickfrancis
Having given some thought to this, I realise that what I really want is a way to find integer values for m such that
where s <= 1. I'm guessing this is a different kettle of fish...

This would appear to mean something like
 N/m  r < c/m^(2  s)
(c = positive constant), which is more easily achievable than having the exponent 2 in the denominator.
There is a notion of "best rational approximations," i.e. fractional approximations which are closer than any fraction with a smaller denominator. These consist of the "intermediate convergents" for the SCF. I know it's somewhere in Chrystal's
Textbook of Algebra, but I'm sure something can be found on line.