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A232986
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Numbers m == 1 (mod 4) such that the Gauss factorial ((m-1)/4, m)! == 1 (mod m).
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1
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5, 145, 205, 725, 1025, 1105, 1145, 1205, 1305, 1313, 1365, 1405, 1469, 1745, 1785, 1845, 1885, 1989, 2145, 2249, 2405, 2465, 2545, 2665, 2745, 2805, 3005, 3045, 3145, 3161, 3205, 3393, 3445, 3485, 3545, 3601, 3625, 3705, 3885, 3893, 3965
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OFFSET
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1,1
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COMMENTS
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The Gauss factorial m_k! is defined to be Product_{1<=j<=m, gcd(j,k)=1} j.
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LINKS
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Table of n, a(n) for n=1..41.
J. B. Cosgrave and K. Dilcher, An introduction to Gauss factorials, Amer. Math. Monthly, 118 (2011), 810-828.
J. B. Cosgrave and K. Dilcher, The Gauss-Wilson theorem for quarter-intervals, Acta Mathematica Hungarica, Sept. 2013.
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EXAMPLE
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m=145 is a term, because 36_145! = 32577412307818387955599294857216 == 1 (mod 145).
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MAPLE
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Gf:=proc(N, n) local j, k; k:=1;
for j from 1 to N do if gcd(j, n)=1 then k:=j*k; fi; od; k; end;
t1:=[];
for i from 1 to 1000 do
n:=4*i+1; if (Gf(i, n) mod n ) = 1 then t1:=[op(t1), n]; fi;
od:
t1;
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CROSSREFS
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Sequence in context: A320414 A168041 A081322 * A322954 A254711 A273920
Adjacent sequences: A232983 A232984 A232985 * A232987 A232988 A232989
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Dec 08 2013
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STATUS
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approved
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