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Ordered Fractions

Assume that the irreducible fractions between 0 and 1, with denominators
at most 99, are listed in ascending order. Determine which two fractions
are adjacent to 11/21 in this listing.
Determine which two fractions are adjacent to 34/87 in this listing.

Is it possible to generalize this to finding the fractions adjacent to a/b?

Source: Modified from Problem 2/3/12 at the
USA Mathematical Talent Search.

Solution

Mail to Ken