In number theory, Zolotarev's lemma states that the Legendre symbol {\displaystyle \left} for an integer a modulo an odd prime number p, where p does not divide a, can be computed as the sign of a permutation: = ε {\displaystyle \left=\varepsilon } where ε denotes the signature of a permutation and πa is the permutation of the nonzero residue classes mod p induced by multiplication by a. Wikipedia