If you can evaluate all three factors, you know whether or not 15 is a quadratic residue mod p.
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On the other hand, the Kronecker symbol does not have the same connection to quadratic residues as the Jacobi symbol.
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The fact that there are quadratic residues and the same number of nonresidues ( mod ) is proved in the article quadratic residue.
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The fact that there are quadratic residues and the same number of nonresidues ( mod ) is proved in the article quadratic residue.
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This result can be achieved if y = 2, 3 ( Quadratic residues can be looked up in the 2nd column ).
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Given integers a and T, a is said to be a " quadratic residue modulo T " if there exists an integer b such that
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As 1 is a quadratic residue modulo n ( n > 1 ), there can be no complete covering system of modular identities for all n.
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Pretty much as the question says, what is the best way to find all odd primes p such that 15 is a quadratic residue modulo p?
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In general, to determine if " a " is a quadratic residue modulo composite " n ", one can use the following theorem:
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When compared to each other, progressions with a quadratic nonresidue remainder have typically slightly more elements than those with a quadratic residue remainder ( Chebyshev's bias ).
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