Ponder This

September 2003

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Ponder This Challenge:

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 e^x. When n is odd, this polynomial has one real root. Prove that this root is irrational for all odd n>1.

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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)

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