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From: gmf@uvacs.UUCP
Newsgroups: net.math
Subject: n! = k**2 problem
Message-ID: <1207@uvacs.UUCP>
Date: Sat, 24-Mar-84 15:15:22 EST
Article-I.D.: uvacs.1207
Posted: Sat Mar 24 15:15:22 1984
Date-Received: Wed, 28-Mar-84 01:05:47 EST
Lines: 16


From
Elementary Theory of Numbers
by  W. Sierpinski (Warsaw, 1964):

p. 138:
"Corollary 4.  For natural numbers > 1 number n! is not a k-th power
with k > 1 being a natural number."

Sierpinski gets this from a theorem of Tchebycheff, p. 137:  "If n is
a natural number > 3, then between n and 2n-2 there is at least one
prime number."  This in turn is obtained from: "If n is a natural
number > 5, then between n and 2n there are at least two different
prime numbers" (p. 137).

           G. Fisher