Dear Mr Gosper (I hope that it is indeed you who receives this) In an email correspondence with Hendrik Lenstra we proved, by accident, something amusing about continued fractions that I do not remember seeing anywhere, but maybe this is well-known to you? (I think you are one of the few remaining experts on continued fractions) If so can you please point us in the right direction. The result is as follows: Let a and b be pairwise coprime positive integers. The sign of the least residue, in absolute value, of a^(-1) mod b EQUALS (-1)^(length of the continued fraction of a/b) Proving these two are equal is trivial by induction, so there is nothing deep here, just amusing. Thanks for any references you can give Andrew Granville