About cookies on this site Our websites require some cookies to function properly (required). In addition, other cookies may be used with your consent to analyze site usage, improve the user experience and for advertising. For more information, please review your options. By visiting our website, you agree to our processing of information as described in IBM’sprivacy statement. To provide a smooth navigation, your cookie preferences will be shared across the IBM web domains listed here.
September 2003
This month's puzzle was submitted by Peter Beech.
For n>1 let P(x)= 1 + x1/1! + x2/2! + ... + xn/n! be the polynomial of degree n formed from the first n+1 terms of the power series for ex. When n is odd, this polynomial has one real root. Prove that this root is irrational for all odd n>1.
We will post the names of those who submit a correct, original solution! If you don't want your name posted then please include such a statement in your submission!
We invite visitors to our website to submit an elegant solution. Send your submission to the ponder@il.ibm.com.
If you have any problems you think we might enjoy, please send them in. All replies should be sent to: ponder@il.ibm.com
Challenge:
09/03/03 @ 01:00 PM ET
Solution:
09/30/03 @ 01:00 PM ET
List Updated:
People who answered correctly:
Hagen von Eitzen (9.3.2003 @04:52:39 PM EDT)
Coserea Gheorghe (9.4.2003 @01:17:52 PM EDT)
Iqstar (9.4.2003 @05:00:00 PM EDT)
Dave Blackston (9.5.2003 @03:06:17 PM EDT)
David Friedman (9.5.2003 @03:48:21 PM EDT)
Joseph DeVincentis (9.5.2003 @10:05:42 PM EDT)
Patrick J. LoPresti (9.6.2003 @01:30:34 PM EDT)
Henry Shin (9.6.2003 @09:27:03 PM EDT)
Dmitry Litvinenko (9.6.2003 @01:32:27 AM EDT)
Dan Dima (9.8.2003 @10:45:50 AM EDT)
Mihai Cioc (9.9.2003 @12:03:32 PM EDT)
John G. Fletcher (9.9.2003 @09:14:17 PM EDT)
Ilan Algor (9.10.2003 @02:45:36 AM EDT)
Surendar Nanchary (9.10.2003 @11:59:00 AM EDT)
Francis Golding (9.10.2003 @12:10:47 PM EDT)
Clive Tong (9.10.2003 @04:34:00 PM EDT)
Andreas Knappe (9.15.2003 @04:19:00 AM EDT)
Karl D'Sousa (9.15.2003 @11:44:00 AM EDT)
R. Nandakumar (9.16.2003 @09:54:03 AM EDT)
Vineet Gupta (9.16.2003 @06:50:37 PM EDT)
Peter Huggins (9.17.2003 @05:43:53 PM EDT)
David Woodruff (9.19.2003 @08:56:23 PM EDT)
Sarang Aravamuthan (9.20.2003 @02:18:00 PM EDT)
Frank Mullin (9.24.2003 @09:20:32 AM EDT)
Attention: If your name is posted here and you wish it removed please send email to the ponder@il.ibm.com.