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A038893
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Odd primes p such that 21 is a square mod p.
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4
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3, 5, 7, 17, 37, 41, 43, 47, 59, 67, 79, 83, 89, 101, 109, 127, 131, 151, 163, 167, 173, 193, 211, 227, 251, 257, 269, 277, 293, 311, 331, 337, 353, 373, 379, 383, 419, 421, 457, 461, 463, 467, 479, 487, 499, 503
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OFFSET
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1,1
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COMMENTS
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These primes correspond to the representation of the two classes of discriminant 21 of binary quadratic forms with principal reduced forms [1, 3, -3] and [3, 3, -1]. The first class represents the primes given in A141159 (or A139492). The second class gives the prime 3 (which divides 21), and primes congruent to 2 (mod 3) and also to 3, 5, 6 (mod 7). The solution of x^2 - 21 == 0 (mod p) leads to the representative primitive parallel forms for discriminant 21 and representation of primes p. - Wolfdieter Lang, Jun 19 2019
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LINKS
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MATHEMATICA
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Select[Prime[Range[100]], JacobiSymbol[21, #] != -1 &] (* Vincenzo Librandi, Sep 07 2012 *)
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PROG
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(PARI) isok(p) = (p>2) && isprime(p) && issquare(Mod(21, p)); \\ Michel Marcus, Jun 19 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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