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 A059770 First solution of x^2 = 2 mod p for primes p such that a solution exists. 3
 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; text; internal format)
 OFFSET 1,2 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). LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..5000 K. Matthews, Finding square roots mod p by Tonelli's algorithm R. Chapman, Square roots modulo a prime 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. 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. MATHEMATICA fQ[n_] := MemberQ[{1, 2, 7}, Mod[n, 8]]; f[n_] := PowerMod[2, 1/2, n]; f@ Select[ Prime[Range], fQ] (* Robert G. Wilson v, Oct 18 2011 *) CROSSREFS Cf. A038873, A059771, A059772. Sequence in context: A259556 A063520 A078677 * A019690 A010620 A046128 Adjacent sequences:  A059767 A059768 A059769 * A059771 A059772 A059773 KEYWORD nonn AUTHOR Klaus Brockhaus, Feb 21 2001 STATUS approved

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Last modified October 18 07:19 EDT 2019. Contains 328146 sequences. (Running on oeis4.)