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A128852
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Anti-elite primes: a prime number p is called anti-elite if only a finite number of Fermat numbers 2^(2^n)+1 are quadratic non-residues mod p.
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2
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2, 13, 17, 97, 193, 241, 257, 641, 673, 769, 2689, 5953, 8929, 12289, 40961, 49921, 61681, 65537, 101377, 114689, 274177, 286721, 319489, 414721, 417793, 550801, 786433, 974849, 1130641, 1376257, 1489153, 1810433, 2424833, 3602561, 6700417
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OFFSET
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1,1
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COMMENTS
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There are infinitely many anti-elite primes.
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REFERENCES
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Alexander Aigner; Über Primzahlen, nach denen (fast) alle Fermatzahlen quadratische Nichtreste sind. Monatsh. Math. 101 (1986), pp. 85-93
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LINKS
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EXAMPLE
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Let F_r:=2^(2^r)+1 = r-th Fermat number. Then a(2)=13 because for all r>1 we have F_r == 4 (mod 13) if r is even, resp. F_r == 10 (mod 13) if r is odd. Notice that 4 and 10 are quadratic residues modulo 13.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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