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A070182 Primes p such that x^5 = 2 has a solution mod p, but x^(5^2) = 2 has no solution mod p. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..35.

PROG

(PARI) forprime(p=2, 47000, x=0; while(x<p&&x^5%p!=2%p, x++); if(x<p, y=0; while(y<p&&y^(5^2)%p!=2%p, y++); if(y==p, print1(p, ", "))))

(MAGMA) [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)

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 */

CROSSREFS

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

Sequence in context: A059858 A152310 A276264 * A100200 A142575 A142657

Adjacent sequences:  A070179 A070180 A070181 * A070183 A070184 A070185

KEYWORD

nonn,easy

AUTHOR

Klaus Brockhaus, Apr 29 2002

STATUS

approved

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Last modified August 5 22:04 EDT 2020. Contains 336214 sequences. (Running on oeis4.)