[math-fun] (x^6-1)/(x^2-x+1) via pebbles
Can anyone steer me toward an online (You-tube?) video of someone using pebble-moves to prove that x^6 - 1 is a multiple of x^2 - x + 1, by starting with a single pebble and managing to move it six spaces to the left (or maybe it was to the right?) with moves that replace a pebble at n with pebble at each of n-1 and n+1, and other moves that do the reverse? Thanks, Jim Propp
On Thu, Jul 16, 2009 at 10:24 AM, James Propp<jpropp@cs.uml.edu> wrote:
Can anyone steer me toward an online (You-tube?) video of someone using pebble-moves to prove that x^6 - 1 is a multiple of x^2 - x + 1, by starting with a single pebble and managing to move it six spaces to the left (or maybe it was to the right?) with moves that replace a pebble at n with pebble at each of n-1 and n+1, and other moves that do the reverse?
http://www.mathlesstraveled.com/?p=80 http://www.mathlesstraveled.com/?p=81 http://www.mathlesstraveled.com/?p=82 The video you mention is linked in the second of these blog entries, I believe. Enjoy, --Joshua Zucker
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James Propp -
Joshua Zucker