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%I #19 Feb 08 2023 07:42:40
%S 193,313,433,577,601,673,769,937,1201,1297,1321,1657,1801,1993,2137,
%T 2473,2521,2593,2833,2953,3169,3529,3673,3697,3769,3889,4057,4129,
%U 4153,4297,4441,4513,4561,4801,4969,5113,5209,5233,5281,5449,5521
%N 3 and -3 are both 4th powers (one implies other) mod these primes p=1 mod 8.
%H Robert Israel, <a href="/A014755/b014755.txt">Table of n, a(n) for n = 1..10000</a>
%p filter:= proc(p) isprime(p) and [msolve(x^4=3, p)] <> [] end proc:
%p select(filter, [seq(i,i=1..10^4, 8)]); # _Robert Israel_, May 07 2019
%t okQ[p_] := PrimeQ[p] && Solve[x^4 == 3, x, Modulus -> p] != {};
%t Select[Range[1, 10000, 8], okQ] (* _Jean-François Alcover_, Feb 08 2023 *)
%o (PARI) forprime(p=1,9999,p%8==1&&ispower(Mod(3,p),4)&&print1(p",")) \\ _M. F. Hasler_, Feb 18 2014
%o (PARI) is_A014755(p)={p%8==1&&ispower(Mod(3,p),4)&&isprime(p)} \\ _M. F. Hasler_, Feb 18 2014
%Y Cf. A007519.
%K nonn
%O 1,1
%A _Warren D. Smith_
%E Offset changed from 0 to 1 by _Bruno Berselli_, Feb 20 2014
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