[math-fun] Harding's Theorem
Puzzle: How much can you learn about hyperfactorials modulo a prime P? What is 1! 2! ... (P-1)! mod P? mod P^2? What about 1^1 * 2^2 * 3^3 * ... * (P-1)^(P-1)? What looks true, and what can you prove? To give everyone a chance to play, lets hold off reporting until noon tomorrow. That's Wednesday, May 9, noon Mountain Daylight Time. (God's own time zone :-).) Rich
On Tue, May 8, 2012 at 8:35 AM, <rcs@xmission.com> wrote:
Puzzle: How much can you learn about hyperfactorials modulo a prime P? What is 1! 2! ... (P-1)! mod P? mod P^2? What about 1^1 * 2^2 * 3^3 * ... * (P-1)^(P-1)? What looks true, and what can you prove?
To give everyone a chance to play, lets hold off reporting until noon tomorrow. That's Wednesday, May 9, noon Mountain Daylight Time. (God's own time zone :-).)
Wow, that's a Mormon catchphrase if I ever heard one. -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
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