JacobiSymbol[Subscript[a, 1], Subscript[c, 1]] JacobiSymbol[Subscript[a, 2], Subscript[c, 2]] JacobiSymbol[Subscript[a, 3], Subscript[c, 3]] == (-1)^((Subscript[c, 1] Subscript[c, 2] + Subscript[c, 1] Subscript[c, 3] + Subscript[c, 2] Subscript[c, 3])/4) /; {{Subscript[a, 1], Subscript[b, 1]}, {Subscript[c, 1], Subscript[d, 1]}} . {{Subscript[a, 2], Subscript[b, 2]}, {Subscript[c, 2], Subscript[d, 2]}} . {{Subscript[a, 3], Subscript[b, 3]}, {Subscript[c, 3], Subscript[d, 3]}} == {{1, 0}, {0, 1}} && Subscript[a, 1] Subscript[d, 1] - Subscript[b, 1] Subscript[c, 1] == 1 && Subscript[a, 2] Subscript[d, 2] - Subscript[b, 2] Subscript[c, 2] == 1 && Subscript[a, 3] Subscript[d, 3] - Subscript[b, 3] Subscript[c, 3] == 1 && Element[{Subscript[a, 1], Subscript[b, 1], Subscript[d, 1], Subscript[a, 2], Subscript[b, 2], Subscript[d, 2], Subscript[a, 3], Subscript[b, 3], Subscript[d, 3]}, Integers] && Element[{(Subscript[c, 1] + 1)/2, (Subscript[c, 2] + 1)/2, (Subscript[c, 3] + 1)/2}, Integers] && Subscript[c, 1] > 0 && Subscript[c, 2] > 0 && Subscript[c, 3] > 0

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<msub> <mi> a </mi> <mn> 3 </mn> </msub> <mo> &#8290; </mo> <msub> <mi> d </mi> <mn> 3 </mn> </msub> </mrow> <mo> - </mo> <mrow> <msub> <mi> b </mi> <mn> 3 </mn> </msub> <mo> &#8290; </mo> <msub> <mi> c </mi> <mn> 3 </mn> </msub> </mrow> </mrow> <mo> &#10869; </mo> <mn> 1 </mn> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <mo> { </mo> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> d </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> , </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> , </mo> <msub> <mi> d </mi> <mn> 2 </mn> </msub> <mo> , </mo> <msub> <mi> a </mi> <mn> 3 </mn> </msub> <mo> , </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> <mo> , </mo> <msub> <mi> d </mi> <mn> 3 </mn> </msub> </mrow> <mo> } </mo> </mrow> <mo> &#8712; </mo> <semantics> <mi> &#8484; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalZ]&quot;, Function[Integers]] 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2001-10-29