A275777 - OEIS

%I #40 Sep 12 2016 10:55:02

%S 7,23,31,79,167,431,479,983,1303,1607,1871,2351,4799,6263,6271,9551,

%T 10103,10111,11471,11519,12503,12647,12959,14087,17231,17623,21599,

%U 23039,25391,25919,25951,28879,29927,33599,35543,43711,48479,48647,49871,56671,57119,62743,71551,71999,79151,81551,82567,91703,96079,97919

%N Primes p such that there are exactly p solutions to y^2 + x*y + y == x^3 + x^2 - 10*x - 10 (mod p).

%C Primes p = prime(n) for which A275742(n) = p.

%C Primes p for which A030184(p) == 0 (mod p).

%C Primes prime(A275745(n)) for which A275745(n) = 0.

%o (PARI)

%o { N = 10^5 + 2;

%o default(seriesprecision,N);

%o V = Vec( eta(q) * eta(q^3) * eta(q^5) * eta(q^15) );

%o forprime(p=2,N, if( V[p]%p == 0, print1(p,", ") ) );

%o } \\ _Joerg Arndt_, Sep 11 2016

%o (PARI) \\ Much slower than the above, but maybe useful for isolated values

%o is(n)=if(!isprime(n), return(0)); my(s,t,y='y); for(x=1,n, s+=#polrootsmod(y^2+x*y+y-x^3-x^2+10*x+10,n); if(s>n, return(0))); s==n \\ _Charles R Greathouse IV_, Sep 12 2016

%Y Cf. A030184, A275742, A275745.

%K nonn

%O 1,1

%A _Seiichi Manyama_, Sep 10 2016

%E More terms from _Joerg Arndt_, Sep 11 2016