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A270800
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Septic artiads: primes p congruent to 1 mod 14 for which all solutions of the congruence x^3 + x^2 - 2x - 1 == 0 (mod p) are 7th power residues.
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7
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14197, 21617, 23801, 24977, 25999, 34763, 37549, 41959, 42407, 45053, 45599, 54713, 55987, 56099, 60271, 61657, 63463, 66067, 72577, 75307, 76343, 76777, 79283, 83357, 88397, 90469, 91309, 99611, 107927, 111217, 111301, 111791, 124699, 126127, 131251, 132287
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OFFSET
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1,1
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LINKS
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E. Lehmer, Artiads characterized, J. Math. Anal. Appl. 15 1966 118-131. See page 126 (but beware errors).
E. Lehmer, Artiads characterized, J. Math. Anal. Appl. 15 1966 118-131 [annotated and corrected scanned copy]
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PROG
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(Sage)
def is_septic_artiad(n) :
if not (n % 14 == 1 and is_prime(n)) : return False
R.<t> = PolynomialRing(GF(n))
return all(r[0]^((n-1)//7) == 1 for r in (t^3 + t^2 - 2*t - 1).roots())
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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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Definition added and sequence extended and corrected by Eric M. Schmidt, Apr 02 2016
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STATUS
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approved
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