Oh, sorry  I didn't realise that. My cableaccess is set up such that the machine appears in the IPrange of CalTech and is, in effect, a member f the CalTech network for all intents and purposes  with the attendant benefit that I can get to all kinds of online journals and such.
To outline the procedure: you can do the whole operation modulo 89. There's the usual rules of modular arithmetic to observe, but this keeps the size of all numbers extremely manageable.
The problem is presented for the case where the individual terms are squares and cubes (like the one in this thread) and the solution is shown for the case of squares (where the 43rd term is not an integer) and then a comment is made that the same procedure working mod89 shows that the 89th term isn't integer in the cubecase.
If it helps, the author (Richard K. Guy) gives as a reference his own book "Unsolved problems in number theory" (Springer 1981), E15. If you're lucky, that might be available at your local library...
