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.

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

Offset: 1

Author

N. J. A. Sloane, Apr 01 2016

Keywords

• nonn

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]

Crossrefs

Cf. A001583.

Programs

Sage

def is_septic_artiad(n) :
    if not (n % 14 == 1 and is_prime(n)) : return False
    R. = 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

Extensions

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