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A344202
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Primes p such that gcd(ord_p(2), ord_p(3)) = 1.
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0
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683, 599479, 108390409, 149817457, 666591179, 2000634731, 4562284561, 14764460089, 24040333283, 2506025630791, 5988931115977
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OFFSET
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1,1
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COMMENTS
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Related to Diophantine equations of the form (2^x-1)*(3^y-1) = n*z^2.
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LINKS
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MATHEMATICA
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Select[Range[10^6], PrimeQ[#] && CoprimeQ[MultiplicativeOrder[2, #], MultiplicativeOrder[3, #]] &] (* Amiram Eldar, May 11 2021 *)
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PROG
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(C++) see link
(PARI) isok(p) = isprime(p) && (gcd(znorder(Mod(2, p)), znorder(Mod(3, p))) == 1); \\ Michel Marcus, May 11 2021
(Python)
from sympy.ntheory import n_order
from sympy import gcd, nextprime
while p < 10**9:
if gcd(n_order(2, p), n_order(3, p)) == 1:
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CROSSREFS
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KEYWORD
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nonn,more,hard
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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