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From: gmf@uvacs.UUCP
Newsgroups: net.math
Subject: Proof wanted
Message-ID: <1273@uvacs.UUCP>
Date: Tue, 1-May-84 21:25:26 EDT
Article-I.D.: uvacs.1273
Posted: Tue May  1 21:25:26 1984
Date-Received: Thu, 3-May-84 08:20:42 EDT
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Concerning  x odd & >= 3  -->  x = 2^k + p for some k and prime p .

This may be relevant:

"It can be proved that for every natural number k there are infinitely
many k-powers of natural numbers which are not of the form a^k + p,
where a is an integer and p a prime. (cf. Clement [2])."
                          W. Sierpinski
                          * Elementary Theory of Numbers *
                          (Warsaw, 1964), p. 113

"Clement, P. A. ...
   [2] Representation of integers in the form: a k-th power plus a prime,
       Amer. Math. Monthly 56 (1949), p. 561."
                          Ibid., p. 450

          Gordon Fisher