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Jacobi symbol

Let a is an integer and n an odd number. Let that the n is equal to p1ⁿ¹p2ⁿ²...pk^nk The Jacobi symbol denoted by (a/n) is defined as
(a/n)=(a/p1)ⁿ¹(a/p2)ⁿ² ... (a/pk)^nk
where (a/pi) is the Legendre symbol (i=1,2,...,k).

If (a/n)=-1 then a is not quadratic residual modn.
If (a/n)=1 we cannot conclude.

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