+49 Again, please private message me the answer!
Let n be an integer greater than 0. The numbers 1,2,3....,n are written on a blackboard. We decide to erase from the blackboard any two numbers, and replace them with their nonnegative difference. After this is done several times, a single number remains on the blackboard. For which values of N can this number equal 0?
Hint(s):
Hint #1: Try small cases.
Hint #2: To rule out a value of n, consider parity. (This means look at whether the number is even or odd.) As a function of n, can you say something about the parity of the last number that remains?
Hint #3: To show that it's possible for a value of n, you may want to try to build on smaller values of n. What proof technique does this suggest?
