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A373468
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Primes such that x^16 = 2 has a solution in Z/pZ, but x^32 = 2 does not.
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0
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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
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OFFSET
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1,1
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LINKS
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EXAMPLE
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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).
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PROG
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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
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CROSSREFS
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Cf. A059287 (similar for x^8 vs x^16).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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