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A270800 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. 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Eric M. Schmidt, Table of n, a(n) for n = 1..1000

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]

PROG

(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())

# Eric M. Schmidt, Apr 02 2016

CROSSREFS

Cf. A001583.

Sequence in context: A258532 A258525 A254917 * A271247 A212949 A205202

Adjacent sequences:  A270797 A270798 A270799 * A270801 A270802 A270803

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Apr 01 2016

EXTENSIONS

Definition added and sequence extended and corrected by Eric M. Schmidt, Apr 02 2016

STATUS

approved

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Last modified April 5 23:04 EDT 2020. Contains 333260 sequences. (Running on oeis4.)