A275773 Primes p congruent to 1 modulo 13 such that x^13 = 2 has a solution modulo p.

4421, 4733, 5669, 5981, 8581, 9413, 10453, 11597, 13963, 14327, 14951, 19267, 22699, 22907, 23557, 25117, 25819, 26417, 28627, 31799, 32579, 35491, 37441, 41549, 44773, 44851, 45553, 46619, 46957, 48179, 49297, 49921, 49999, 50207, 52859, 53639, 60217, 64403

Offset: 1

Author

Felix Fröhlich, Aug 08 2016

Keywords

• nonn

Comments

Intersection of A049545 and A268753.

These are the counterexamples mentioned in the Sep 12 2012 comment from Bruno Berselli in A059245.

Examples

			4421 is in the sequence since it is prime, it is congruent to 1 (mod 13), and x^13 == 2 (mod 4421) has the solution x = 162. - _Michael B. Porter_, Aug 26 2016
		

Crossrefs

Cf. A049545, A059245, A268753.

Programs

Mathematica

Quiet@ Select[Prime@ Range[10^4], And[Mod[#, 13] == 1, IntegerQ@ PowerMod[2, 1/13, #]] &] (* Michael De Vlieger, Aug 10 2016 *)

PARI

forprime(p=1, 1e6, if(Mod(p, 13)==1 && ispower(Mod(2, p), 13), print1(p, ", ")))