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 A040121 Primes p such that x^4 = 10 has no solution mod p. 2

%I #11 Sep 08 2022 08:44:53

%S 7,11,13,17,19,23,29,47,59,61,73,89,97,101,103,109,113,127,131,137,

%T 139,149,157,167,179,181,193,197,211,223,229,233,251,257,263,269,281,

%U 293,313,331,337,349,353,367,373

%N Primes p such that x^4 = 10 has no solution mod p.

%C Complement of A040119 relative to A000040. - _Vincenzo Librandi_, Sep 17 2012

%H Vincenzo Librandi, <a href="/A040121/b040121.txt">Table of n, a(n) for n = 1..1000</a>

%t ok[p_]:= Reduce[Mod[x^4 - 10, p] == 0, x, Integers] == False;Select[Prime[Range[100]], ok] (* _Vincenzo Librandi_, Sep 17 2012 *)

%o (Magma) [p: p in PrimesUpTo(500) | not exists{x : x in ResidueClassRing(p) | x^4 eq 10} ]; // _Vincenzo Librandi_, Sep 17 2012

%o (PARI) is(p)=!ispower(Mod(10,p),4) && isprime(p)

%o select(is, primes(100)) \\ _Charles R Greathouse IV_, Aug 10 2022

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_.

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Last modified October 4 23:18 EDT 2023. Contains 365888 sequences. (Running on oeis4.)