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A191055
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Primes p that have Kronecker symbol (p|93) = 1.
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1
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7, 11, 17, 19, 23, 29, 53, 67, 83, 89, 97, 103, 109, 137, 157, 163, 167, 179, 193, 197, 211, 239, 251, 263, 269, 283, 307, 347, 349, 353, 373, 379, 383, 389, 397, 401, 421, 439, 449, 461, 491, 509, 541, 547, 557, 569, 577, 587, 607, 641, 647, 661, 677, 691
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OFFSET
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1,1
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COMMENTS
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Originally erroneously named "Primes that are squares mod 93".
Equivalently, primes p such that kronecker(93,p) = 1.
Rational primes that decompose in the field Q(sqrt(93)).
Primes congruent to 1, 2, 4, 7, 8, 11, 13, 14, 16, 17, 22, 25, 26, 28, 32, 34, 41, 44, 47, 49, 50, 52, 56, 64, 67, 68, 77, 82 modulo 87. (End)
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LINKS
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MATHEMATICA
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Select[Prime[Range[200]], JacobiSymbol[#, 93]==1&]
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PROG
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(Magma) [p: p in PrimesUpTo(691) | JacobiSymbol(p, 93) eq 1]; // Vincenzo Librandi, Sep 10 2012
(PARI) isA191055(p) == isprime(p) && kronecker(p, 93) == 1 \\ Jianing Song, Oct 13 2022
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CROSSREFS
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A038981, the sequence of primes that do not remain inert in the field Q(sqrt(93)), is essentially the same.
Cf. A038982 (rational primes that remain inert in the field Q(sqrt(93)))..
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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