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%I #28 Nov 21 2021 13:36:17
%S 61,67,73,103,151,193,271,307,367,439,499,523,547,577,613,619,643,661,
%T 727,757,787,853,919,967,991,997,1009,1021,1093,1117,1249,1303,1321,
%U 1399,1531,1543,1549,1597,1609,1621,1669,1759,1783,1861,1867
%N Primes p==1 (mod 6) such that 3 and -3 are both cubes (one implies other) modulo p.
%C Primes of the form x^2+xy+61y^2, whose discriminant is -243. - _T. D. Noe_, May 17 2005
%C Primes of the form (x^2 + 243*y^2)/4. - _Arkadiusz Wesolowski_, May 30 2015
%D K. Ireland and M. Rosen, A classical introduction to modern number theory, Vol. 84, Graduate Texts in Mathematics, Springer-Verlag. Exercise 23, p. 135.
%H Bruno Berselli, <a href="/A014753/b014753.txt">Table of n, a(n) for n = 1..1000</a>
%t p6 = Select[6*Range[0, 400]+1, PrimeQ]; Select[p6, (Reduce[3 == k^3+m*#, {k, m}, Integers] =!= False)&] (* _Jean-François Alcover_, Feb 20 2014 *)
%o (PARI) forprime(p=1, 9999, p%6==1&&ispower(Mod(3, p), 3)&&print1(p", ")) \\ _M. F. Hasler_, Feb 18 2014
%o (PARI) is_A014753(p)={p%6==1&&ispower(Mod(3, p), 3)&&isprime(p)} \\ _M. F. Hasler_, Feb 18 2014
%Y Cf. A014752, A014755.
%K nonn,easy
%O 1,1
%A _Warren D. Smith_
%E Offset changed from 0 to 1 by _Bruno Berselli_, Feb 20 2014
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