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Given an integer ${\displaystyle a}$ and an odd prime ${\displaystyle p}$, the former is a quadratic nonresidue of the latter if the congruence ${\displaystyle x^{2}\equiv a\mod p}$ does not have a solution. For example, 5 is a quadratic nonresidue of 7 because ${\displaystyle x^{2}\equiv 5\mod 7}$ has no solutions.