Search: id:A059770
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%I A059770
%S A059770 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,
%T A059770 60,110,96,132,66,120,26,167,19,79,137,53,97,188,206,21,30,80,203,187,
%U A059770 91,157,249,201,34,142,166,222,194,296,94,67,36,283,324,27,102,113,73
%N A059770 First solution of x^2 = 2 mod p for primes p such that a solution exists.
%C A059770 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).
%H A059770 K. Matthews, <a href="http://www.numbertheory.org/php/tonelli.html">Finding 
               square roots mod p by Tonelli's algorithm</a>
%H A059770 R. Chapman, <a href="http://www.maths.ex.ac.uk/~rjc/courses/nt03/sqrt.pdf">
               Square roots modulo a prime</a>
%F A059770 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.
%e A059770 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.
%Y A059770 Cf. A038873, A059771, A059772.
%Y A059770 Sequence in context: A082284 A063520 A078677 this_sequence A019690 A010620 
               A046128
%Y A059770 Adjacent sequences: A059767 A059768 A059769 this_sequence A059771 A059772 
               A059773
%K A059770 nonn
%O A059770 1,2
%A A059770 Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Feb 21 2001

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