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A177860
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Product of the quadratic residues of prime(n).
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2
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1, 1, 4, 8, 540, 12960, 1797120, 22619520, 465813504, 267346759680000, 216218419200000, 199658024013127680000, 136256285631578112000000, 12446179270879850496000000, 34611344543529418987929600
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OFFSET
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1,3
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COMMENTS
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a(n) == (-1)^((p+1)/2) (mod p), if p = prime(n) is odd.
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REFERENCES
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Carl-Erik Froeberg, On sums and products of quadratic residues, BIT, Nord. Tidskr. Inf.-behandl. 11 (1971) 389-398.
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LINKS
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FORMULA
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a(n) = (p-1)!/A177861(n), where p = prime(n).
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EXAMPLE
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The quadratic residues of prime(4) = 7 are 1, 2, and 4, so a(4) = 1*2*4 = 8.
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MATHEMATICA
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Table[ Apply[Times, Flatten[Position[ Table[JacobiSymbol[i, Prime[n]], {i, 1, Prime[n] - 1}], 1]]], {n, 1, 16}]
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CROSSREFS
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Cf. A076409 Sum of the quadratic residues of prime(n), A177861 Product of the quadratic nonresidues of prime(n), A163366 Product of the quadratic residues of prime(n) modulo prime(n).
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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