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From: leeper@ahutb.UUCP (leeper)
Newsgroups: net.math,net.puzzle
Subject: Exponant Duals
Message-ID: <555@ahutb.UUCP>
Date: Tue, 12-Mar-85 17:01:11 EST
Article-I.D.: ahutb.555
Posted: Tue Mar 12 17:01:11 1985
Date-Received: Thu, 14-Mar-85 05:11:13 EST
Organization: AT&T Information Systems Labs, Holmdel NJ
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Xref: watmath net.math:1899 net.puzzle:590

This is a problem I made up when I was in high school.

Define an "exponant dual" of the x to be some OTHER number y so that

	x^y = y^x

For example an exponant dual of 2 is 4 since 2 is not 4 and 

	2^4 = 4^2 = 16

For what real numbers greater than one do there exist no exponant
duals?  For what real numbers greater than one does there exist one
exponant dual?  For what real numbers greater than one do there exist
more than one exponant dual?

				Mark Leeper
				...ihnp4!ahutb!leeper