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3, 8, 13, 17, 31, 32, 30, 50, 46, 55, 75, 91, 76, 98, 100, 105, 129, 93, 162, 112, 183, 122, 144, 177, 241, 187, 217, 228, 155, 288, 203, 189, 213, 311, 269, 274, 334, 381, 266, 392, 254, 382, 348, 413, 301, 286, 489, 439, 483, 553, 516, 476, 578, 423, 487, 504
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| If we take 4 numbers : 1, A002314(n), A152676(n), A152680(n) then
multiplication table modulo A002144(n) is isomorphc with latin square:
1 2 3 4
2 4 1 3
3 1 4 2
4 3 2 1
and isomorphic with multiplication table of {1,I,-I,-1} where I is Sqrt[ -1],
A152680(n) is isomorphic with -1, A002314(n) with I or -I and A152676(n) vice versa -I or I.
1, A002314(n), A152676(n), A152680(n) are subfield of Galois Field [A002144(n)].
Let p = A002144(n), the n-th prime of the form 4k+1. Then a(n) and A002314(n) are the two square roots of -1 (mod p). Note that a(n) is also the multiplicative inverse of A002314(n) (mod p). - T. D. Noe, Feb 18 2010
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
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MATHEMATICA
| aa = {}; Do[If[Mod[Prime[n], 4] == 1, k = 1; While[ ! Mod[k^2 + 1, Prime[n]] == 0, k++ ]; AppendTo[aa, Prime[n] - k]], {n, 1, 200}]; aa (*Artur Jasinski*)
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CROSSREFS
| A002144, A002314, A152680
Sequence in context: A022807 A187093 A081766 * A197062 A010064 A133330
Adjacent sequences: A152673 A152674 A152675 * A152677 A152678 A152679
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KEYWORD
| nonn
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AUTHOR
| Artur Jasinski (grafix(AT)csl.pl), Dec 10 2008
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