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A045315 Primes p such that x^8 = 2 has a solution mod p. 9
2, 7, 23, 31, 47, 71, 73, 79, 89, 103, 127, 151, 167, 191, 199, 223, 233, 239, 257, 263, 271, 311, 337, 359, 367, 383, 431, 439, 463, 479, 487, 503, 599, 601, 607, 631, 647, 719, 727, 743, 751, 823, 839, 863, 881, 887, 911, 919, 937, 967, 983, 991, 1031, 1039 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Coincides with the sequence of "primes p such that x^16 = 2 has a solution mod p" for first 58 terms (and then diverges).

Complement of A045316 relative to A000040. - Vincenzo Librandi, Sep 13 2012

REFERENCES

A. Aigner, Kriterien zum 8. und 16. Potenzcharakter der Reste 2 und -2, Deutsche Math. 4 (1939), 44-52; FdM 65 - I (1939), 112.

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

H. Hasse, Der 2^n-te Potenzcharakter von 2 im Koerper der 2^n-ten Einheitswurzeln, Rend. Circ. Matem. Palermo (2), 7 (1958), 185-243.

Franz Lemmermeyer, Bibliography on Reciprocity Laws

A. L. Whiteman, The sixteenth power residue character of 2, Canad. J. Math. 6 (1954), 364-373; Zbl 55.27102.

Index entries for related sequences

MATHEMATICA

ok[p_] := Reduce[ Mod[x^8-2, p] == 0, x, Integers] =!= False; Select[ Prime[ Range[200] ], ok] (* Jean-Fran├žois Alcover, Nov 28 2011 *)

PROG

(MAGMA) [p: p in PrimesUpTo(1100) | exists(t){x : x in ResidueClassRing(p) | x^8 eq 2}]; // Vincenzo Librandi, Sep 13 2012

(PARI) is(n)=isprime(n) && ispower(Mod(2, n), 8) \\ Charles R Greathouse IV, Feb 08 2017

CROSSREFS

Cf. A000040, A001132, A040028, A040098, A045316.

Sequence in context: A309580 A186098 A040098 * A072935 A049564 A072936

Adjacent sequences:  A045312 A045313 A045314 * A045316 A045317 A045318

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified May 10 22:35 EDT 2021. Contains 343780 sequences. (Running on oeis4.)