Solve Problem 1 of Project Euler without using unary numbers

[Smaug123]

• [x] Show that Z is a Euclidean domain.
• [ ] Show that Euclidean domains are UFDs.
• [ ] Define "binary Z".
• [ ] Show that "binary Z" is isomorphic to Z, and hence is a Euclidean domain, and hence is a UFD.
• [ ] Rephrase the solution to Problem 1 of Project Euler in terms of binary Z. (This final step should be extremely easy, if the earlier steps have been done correctly.)

For bonus marks, see if this makes the solution any faster than unary!