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A260072
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Primes p such that (p-1)^2+1 divides 2^(p-1)-1.
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2
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OFFSET
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1,1
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COMMENTS
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a(6), if it exists, is larger than 1.7*10^12. - Giovanni Resta, Jul 23 2015
N = 1382401 is the smallest composite number such that (n-1)^2+1 divides 2^(n-1)-1, cf. A260407; see also A081762 and A260406. The sequence contains all Fermat primes 2^2^k+1 > 5 (A019434). - M. F. Hasler, Jul 24 2015
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LINKS
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EXAMPLE
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17 is in this sequence because (17 - 1)^2 + 1 = 257 divides 2^(17 - 1) - 1 = 65535; 65535 / 257 = 255.
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MATHEMATICA
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fQ[n_] := PowerMod[2, n-1, (n-1)^2 + 1] == 1; p = 2; lst = {}; While[p < 10^9, If[ fQ@ p, AppendTo[lst, p]]; p = NextPrime@ p] (* Robert G. Wilson v, Jul 24 2015 *)
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PROG
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(Magma) [n: n in [1..2000000] | IsPrime(n) and (2^(n-1)-1) mod ((n-1)^2 + 1) eq 0]
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CROSSREFS
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Cf. A081762 (primes p such that (p-1)^2 - 1 divides 2^(p-1) - 1).
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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