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A252279
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Primes p congruent to 1 mod 16 such that x^8 = 2 has a solution mod p.
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1
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257, 337, 881, 1217, 1249, 1553, 1777, 2113, 2593, 2657, 2833, 4049, 4177, 4273, 4481, 4513, 4721, 4993, 5297, 6353, 6449, 6481, 6529, 6689, 7121, 7489, 8081, 8609, 9137, 9281, 9649, 10177, 10337, 10369, 10433, 10657, 11329, 11617, 11633, 12049, 12241, 12577
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OFFSET
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1,1
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COMMENTS
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For a prime p congruent to 1 mod 16, the number 2 is an octavic residue mod p if and only if there are integers x and y such that x^2 + 256*y^2 = p.
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LINKS
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PROG
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(Magma) [p: p in PrimesUpTo(12577) | p mod 16 eq 1 and exists(t){x : x in ResidueClassRing(p) | x^8 eq 2}]; // Arkadiusz Wesolowski, Dec 19 2020
(PARI) isok(p) = isprime(p) && (Mod(p, 16) == 1) && ispower(Mod(2, p), 8); \\ Michel Marcus, Dec 19 2020
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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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