[math-fun] rationals hard to approximate by rationals

Consider a rational number (in reduced form) X=A/B. Suppose I tell you B, and I ask you to "find A such that X has only 1s and 2s in its partial fraction expansion." (Even better, "...and with the fewest 2s.") For example if B=2^32. You could by brute force just try all 2^32 possible A (actually only 2^31 if we insist A=odd) computing the continued fraction of each A/B, Is there a faster method? How fast can you get? For which (if any) B's is the problem unsolvable? -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)