Proof for Induction

Asked Jun 29 '20 at 01:32

Active Jun 29 '20 at 01:41

Viewed 119 times

Let $n$ be an integer greater than $0.$ The numbers $1, 2, 3, \ldots, n$ 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 $0$?

I've noticed that as long as $n \equiv 0, 3 \pmod 4,$ the number will equal $0.$ However, how do I prove this? Haven't really done any proof problems before.

edited Jun 29 '20 at 01:41

Michael Hardy

asked Jun 29 '20 at 01:32

Robert Mugabe

See https://math.stackexchange.com/questions/3309935/puzzle-remaining-numbers-on-board-erase-2-numbers-but-add-the-difference (which has a much more informative title than you have used here). – Gerry Myerson Jun 29 '20 at 01:53
Was that link helpful? (and will you please edit your title to something more informative?) – Gerry Myerson Jun 30 '20 at 12:32
Are you still here, Robert? – Gerry Myerson Jul 01 '20 at 23:34
I guess not. Bye-bye, Robert! – Gerry Myerson Jul 03 '20 at 13:08

Proof for Induction

0 Answers0