Math 422: Introduction to Number Theory
Homework on 3
1. Silverman 5.4.
2. Silverman 6.1.
3. Silverman 6.3. To prove the program works, show by induction that b
divides both gn − axn and wn − avn. (Incidentally, in Python you don’t
need either of the variables s or t.)
4. Silverman 6.4.
5. Silverman 7.1.
6. Silverman 7.2.
7. Two players play the following game: The numbers 25 and 36 are written
on a board. On each player’s turn, they select any two numbers currently
up and write on the board the positive difference of those two numbers,
provided the difference is not already written on the board. The game
continues until a player cannot write anything down. The last player to
write down a number wins. Does the game always end? If so, assuming
perfect play, who wins?
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