The approximation 2434/2659 can be obtained by using the theory of Continued Fractions. These are formulas of the form

a0+1/(a1+1/(a2+1/(a3+...)))


Sigh... I just wish I were smart enough to really understand that!

But I got what I needed for the fractionization of repeating decimals -- I can never remember that from one year to the next because it seems to me to be so unintuitive. Many thanks to all who helped.

And I'll agree with everyone else who said that it's a stupid way of generating an unlock code.

Well, yes and no. Remember that their objective was to make it easy for them to get in, not necessarily to keep other people out. They stand to lose nothing if some incredibly skilled hacker like myself can see through the amazingly sophisticated algorithm of dividing the answer by the query to get the multiplicand. All I can do with this unlock key is damage my own data. They just want an "out" in case I (or some other curious hacker) does that. They can say "It's not our fault you trashed your data. That'll teach you not to hack our unlock key."

tanstaafl.