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A059770
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First solution of x^2 = 2 mod p for primes p such that a solution exists.
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2
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0, 3, 6, 5, 8, 17, 7, 12, 32, 9, 25, 14, 38, 51, 16, 31, 46, 13, 57, 52, 20, 15, 85, 99, 22, 60, 110, 96, 132, 66, 120, 26, 167, 19, 79, 137, 53, 97, 188, 206, 21, 30, 80, 203, 187, 91, 157, 249, 201, 34, 142, 166, 222, 194, 296, 94, 67, 36, 283, 324, 27, 102, 113, 73
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Solutions mod p are represented by integers from 0 to p-1. For p > 2: If x^2 = 2 has a solution mod p, then it has exactly two solutions and their sum is p; i is a solution mod p of x^2 = 2 iff p-i is a solution mod p of x^2 = 2. No integer occurs more than once in this sequence. Moreover, no integer (except 0) occurs both in this sequence and in sequence A059771 of the second solutions (Cf. A059772).
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LINKS
| K. Matthews, Finding square roots mod p by Tonelli's algorithm
R. Chapman, Square roots modulo a prime
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FORMULA
| a(n) = first (least) solution of x^2 = 2 mod p, where p is the n-th prime such that x^2 = 2 mod p has a solution, i.e. p is the n-th term of A038873.
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EXAMPLE
| a(6) = 17, since 41 is the sixth term of A038873, 17 and 24 are the solutions mod 41 of x^2 = 2 and 17 is the smaller one.
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MATHEMATICA
| fQ[n_] := MemberQ[{1, 2, 7}, Mod[n, 8]]; f[n_] := PowerMod[2, 1/2, n]; f@ Select[ Prime[Range[135]], fQ] (* Robert G. Wilson v, Oct 18 2011 *)
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CROSSREFS
| Cf. A038873, A059771, A059772.
Sequence in context: A082284 A063520 A078677 * A019690 A010620 A046128
Adjacent sequences: A059767 A059768 A059769 * A059771 A059772 A059773
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KEYWORD
| nonn
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AUTHOR
| Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Feb 21 2001
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