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A070181 Primes p such that x^4 = 2 has a solution mod p, but x^(4^2) = 2 has no solution mod p. 2
113, 281, 353, 577, 593, 617, 1033, 1049, 1097, 1153, 1193, 1201, 1217, 1249, 1481, 1553, 1601, 1753, 1777, 1889, 2129, 2273, 2281, 2393, 2473, 2689, 2833, 2857, 3049, 3089, 3121, 3137, 3217, 3313, 3361, 3529, 3673, 3761, 3833, 4001, 4049, 4153, 4217 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..43.

PROG

(PARI) forprime(p=2, 4250, x=0; while(x<p&&x^4%p!=2%p, x++); if(x<p, y=0; while(y<p&&y^(4^2)%p!=2%p, y++); if(y==p, print1(p, ", "))))

(MAGMA) [p: p in PrimesUpTo(5000) | not exists{x: x in ResidueClassRing(p) | x^16 eq 2} and exists{x: x in ResidueClassRing(p) | x^4 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, 4, 4^2), print1(p, ", ")));

/* Joerg Arndt, Sep 21 2012 */

CROSSREFS

Cf. A040098, A045315, A045316, A059667, A070179, A070180, A070182 - A070188.

Sequence in context: A142947 A325067 A142641 * A001134 A070188 A059331

Adjacent sequences:  A070178 A070179 A070180 * A070182 A070183 A070184

KEYWORD

nonn,easy

AUTHOR

Klaus Brockhaus, Apr 29 2002

STATUS

approved

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Last modified October 16 12:23 EDT 2021. Contains 348041 sequences. (Running on oeis4.)