# Minimal fractional representations of integers mod M

We say that the fraction N/D 'represents' x when x * D = N % M.  This
definition admits many possible fractional representations.  We say
that N/D is a 'minimal' representation of x if no smaller denominator
results in a numerator with a magnitude less than N.  This book
introduces a function for computing such fractional representations
and proves that it generates minimal fractions.  We also prove that
every x has a minimal fractional representation in which the magnitude
of N and D are less than or equal to (sqrt M).
