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Squares mod 65537.
5

%I #22 Dec 28 2019 14:33:29

%S 0,1,2,4,8,9,13,15,16,17,18,19,21,25,26,30,32,33,34,35,36,37,38,42,49,

%T 50,52,53,55,60,64,66,68,69,70,71,72,74,76,77,79,81,84,87,93,97,98,

%U 100,103,104,106,107,109,110,115,117,120,121,123,128,129,132,135

%N Squares mod 65537.

%C Because 65537 is a Fermat prime, the complement of this set, A136806, is the set of primitive roots (mod 65537).

%H Nathaniel Johnston, <a href="/A136805/b136805.txt">Table of n, a(n) for n = 1..32769</a> (full sequence)

%H OEIS Wiki, <a href="/index/Sq#squares">Index to sequences related to squares</a>

%F a(n) + a(32771 - n) = 65537 for n > 1.

%p A136805:={}: for n from 0 to 65536 do A136805 := A136805 union {n^2 mod 65537}: od: l:=sort(convert(A136805,list)): l[1..63]; # _Nathaniel Johnston_, Jun 23 2011

%t p = 65537; Select[Range[0, p - 1], JacobiSymbol[#, p] == 1 &]

%o (Sage) [quadratic_residues(65537)] # _Zerinvary Lajos_, May 24 2009

%o (PARI) A136805=Set([k^2 | k <- [0..2^16]]%65537); \\ _M. F. Hasler_, Nov 15 2017

%o (Scala) ((1: BigInt) to (65537: BigInt)).map(n => (n * n) % 65537).toSet.toSeq.sorted // _Alonso del Arte_, Dec 17 2019

%Y Cf. A136806 (nonsquares mod 65537); A136803 and A136804 ((non)squares mod 257).

%Y Cf. A010379.

%K fini,full,easy,nonn

%O 1,3

%A _T. D. Noe_, Jan 22 2008