If irrational x is approximated by rational p/r, and irrational y is approximated by rational q/r, then a hand-waving argument using information conservation shows that there should be lots of approximations good to order r^(-3/2). If we did not require the same r in both denominators, then it is known from continued fraction theory that we could do better, namely r^(-2). Suppose x and y are given with n bits each, for a total of 2n bits. Then integers p, q, r will have (2/3)n bits each. If the fractions are to be good to n bits, then the error is of order r^(-3/2). Is this conjecture known to be true (or false)? __________________________________________________ Do you Yahoo!? Yahoo! Mail Plus - Powerful. Affordable. Sign up now. http://mailplus.yahoo.com