A275777 Primes p such that there are exactly p solutions to y^2 + x*y + y == x^3 + x^2 - 10*x - 10 (mod p).

7, 23, 31, 79, 167, 431, 479, 983, 1303, 1607, 1871, 2351, 4799, 6263, 6271, 9551, 10103, 10111, 11471, 11519, 12503, 12647, 12959, 14087, 17231, 17623, 21599, 23039, 25391, 25919, 25951, 28879, 29927, 33599, 35543, 43711, 48479, 48647, 49871, 56671, 57119, 62743, 71551, 71999, 79151, 81551, 82567, 91703, 96079, 97919

Offset

1,1

Comments

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

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

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

Links

Table of n, a(n) for n=1..50.

Prog

(PARI)
{ N = 10^5 + 2;
default(seriesprecision, N);
V = Vec( eta(q) * eta(q^3) * eta(q^5) * eta(q^15) );
forprime(p=2, N, if( V[p]%p == 0, print1(p, ", ") ) );
} \\ Joerg Arndt, Sep 11 2016
(PARI) \\ Much slower than the above, but maybe useful for isolated values
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

Crossrefs

Cf. A030184, A275742, A275745.

Sequence in context: A141175 A295196 A287309 * A329931 A157811 A341284

Adjacent sequences: A275774 A275775 A275776 * A275778 A275779 A275780

Keyword

nonn

Author

Seiichi Manyama, Sep 10 2016

Extensions

More terms from Joerg Arndt, Sep 11 2016

Status

approved