test: If Mime conversion is working, this message should be plain text. ---- E. M. Wright, an author of Hardy & Wright's Introduction to the Theory of Numbers, died recently. ---- My memory of the rule for when CFs converge: If all partial quotients are positive, then the CF values either converge, or oscillate while approaching two limit points. If the sum of the PQs is infinite, then the CF converges. (Is this right? I think the oscillation interval drops roughly by 1/(1+PQ) for each term, and that product ->0 should be same as sum PQ -> infinity.) Of course this leaves open negative and complex partial quotients. ---- I looked at Dyson's problem. (Show that no power of 2 is the reverse of a power of 5, except 1 = 2^0 = 5^0.) There are some easy partial results: Assume a counterexample. Then both are squares and have an odd number of digits, or both are non-squares and have an even number of digits; both are cubes, or both are non-cubes, and of the opposite sense. These come from looking at the powers mod 9 and mod 11. I tried looking at additional moduli like 7, 13, 101, etc. There are restrictions on various digit-position sums, but nothing easy to state. The 1 solution means that solutions exist mod all primes (except 2,5). My favorite effort in this direction is "2^86 is the last power of 2 without a 0 digit". Rich rcs@cs.arizona.edu