A373468 Primes such that x^16 = 2 has a solution in Z/pZ, but x^32 = 2 does not.
257, 2113, 2657, 7489, 10177, 15073, 18593, 23041, 25121, 25409, 25537, 25793, 27809, 30881, 30977, 32321, 37409, 38273, 41729, 43649, 51137, 51361, 54721, 59809, 63841, 67073, 67489, 75553, 77569, 83009, 86561, 92641, 94049, 94433, 95713, 101281, 102241
Offset: 1
Keywords
Examples
For p = 257, the equation x^16 = 2 has solutions 27, 41, 54, ... in Z/pZ, but x^32 can only be 0, +-1, +-4, +-16, +-64 (mod p).
Crossrefs
Programs
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PARI
select( {is_A373468(p)=Mod(2,p)^(p\gcd(16,p-1))==1&&Mod(2,p)^(p\gcd(32,p-1))!=1}, primes(19999)) -
Python
from itertools import islice from sympy import nextprime, is_nthpow_residue def A373468_gen(startvalue=2): # generator of terms >= startvalue p = max(1,startvalue-1) while (p:=nextprime(p)): if is_nthpow_residue(2,16,p) and not is_nthpow_residue(2,32,p): yield p A373468_list = list(islice(A373468_gen(),10)) # Chai Wah Wu, Jun 23 2024