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A275773 Primes p congruent to 1 modulo 13 such that x^13 = 2 has a solution modulo p. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Intersection of A049545 and A268753.
These are the counterexamples mentioned in the Sep 12 2012 comment from Bruno Berselli in A059245.
LINKS
EXAMPLE
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
MATHEMATICA
Quiet@ Select[Prime@ Range[10^4], And[Mod[#, 13] == 1, IntegerQ@ PowerMod[2, 1/13, #]] &] (* Michael De Vlieger, Aug 10 2016 *)
PROG
(PARI) forprime(p=1, 1e6, if(Mod(p, 13)==1 && ispower(Mod(2, p), 13), print1(p, ", ")))
CROSSREFS
Sequence in context: A116342 A035784 A108008 * A060363 A128194 A184091
KEYWORD
nonn
AUTHOR
Felix Fröhlich, Aug 08 2016
STATUS
approved

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Last modified May 25 09:23 EDT 2024. Contains 372786 sequences. (Running on oeis4.)