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A071713
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a(n) = smallest value of |x^n + y^n + z^n| for x,y,z distinct nonzero integers.
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0
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OFFSET
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1,2
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COMMENTS
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If n is even, a(n)=1+2^n+3^n. Does a(5)=12 ?
The conjectured minimum of 12 for a(5) can be achieved by (x,y,z) = (13,16,-17). - Stefan Steinerberger, Dec 13 2007
Not only must x,y,z, be distinct, but also |x|, |y|, |z|. Otherwise take x = -y and z = 1; then for any odd n, a(n) = |x^n + (-x)^n + 1^n| = 1. - Ryan Propper, Feb 06 2008
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LINKS
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K. S. Brown, A Conjecture on the Fermat Function (in Marginalia)
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CROSSREFS
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KEYWORD
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more,nonn,hard
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AUTHOR
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STATUS
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approved
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