A049557 -id:A049557 - cp's OEIS frontend

A059313 Primes p such that x^25 = 2 has no solution mod p.

11, 31, 41, 61, 71, 101, 131, 151, 181, 191, 211, 251, 271, 281, 311, 331, 401, 421, 461, 491, 521, 541, 601, 631, 661, 691, 701, 751, 761, 811, 821, 881, 941, 991, 1021, 1031, 1051, 1061, 1091, 1151, 1171, 1201, 1231, 1291, 1301, 1321, 1361, 1381, 1451

Offset: 1

Klaus Brockhaus, Jan 25 2001

Complement of A049557 relative to A000040.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A000040, A049557.

[p: p in PrimesUpTo(1500) | forall{x: x in ResidueClassRing(p) | x^25 ne 2}]; // Vincenzo Librandi, Sep 20 2012

ok[p_] := Reduce[Mod[x^25 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[250]], ok ] (* Vincenzo Librandi, Sep 20 2012  *)

A070182 Primes p such that x^5 = 2 has a solution mod p, but x^(5^2) = 2 has no solution mod p.

Original entry on oeis.org

151, 251, 3251, 3301, 4751, 8501, 11251, 11701, 13751, 14251, 14951, 15551, 16451, 17401, 18401, 21401, 21601, 24251, 28351, 28901, 32251, 32401, 32801, 34301, 36151, 36451, 37201, 40351, 42451, 42701, 44201, 45751, 46051, 46451, 46901

Offset: 1

Klaus Brockhaus, Apr 29 2002

Cf. A040159, A049557, A059313, A059667, A070179 - A070181, A070183 - A070188.

[p: p in PrimesUpTo(50000) | not exists{x: x in ResidueClassRing(p) | x^25 eq 2} and exists{x: x in ResidueClassRing(p) | x^5 eq 2}]; // Vincenzo Librandi, Sep 21 2012

PARI
```
forprime(p=2,47000,x=0; while(x
				
```

ok(p, r, k1, k2)={
    if (  Mod(r,p)^((p-1)/gcd(k1,p-1))!=1, return(0) );
    if (  Mod(r,p)^((p-1)/gcd(k2,p-1))==1, return(0) );
    return(1);
}
forprime(p=2,10^5, if (ok(p,2,5,5^2),print1(p,", ")));
/* Joerg Arndt, Sep 21 2012 */

cp's OEIS Frontend

A059313 Primes p such that x^25 = 2 has no solution mod p.

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