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gptkbp:instanceOf
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gptkb:mathematical_concept
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gptkbp:application
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Random number generation
Hash functions
Pseudorandom generators
Public-key cryptosystems
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gptkbp:definedIn
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Integers congruent to a perfect square modulo n
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gptkbp:opposedBy
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Quadratic nonresidues
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gptkbp:property
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0 is always a quadratic residue modulo n
1 is always a quadratic residue modulo n
For an odd prime p, there are (p-1)/2 quadratic residues modulo p
If x is a quadratic residue modulo n, then there exists y such that y^2 ≡ x (mod n)
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gptkbp:relatedTo
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gptkb:Modular_arithmetic
gptkb:Multiplicative_group_modulo_n
gptkb:Number_theory
gptkb:Euler's_criterion
gptkb:Tonelli–Shanks_algorithm
Finite fields
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gptkbp:studiedBy
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gptkb:Carl_Friedrich_Gauss
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gptkbp:symbol
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gptkb:Legendre_symbol
Jacobi symbol
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gptkbp:usedIn
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gptkb:Quadratic_reciprocity
gptkb:Algebraic_number_theory
Cryptography
Primality testing
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gptkbp:bfsParent
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gptkb:Quadratic_reciprocity
gptkb:Euler's_criterion
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gptkbp:bfsLayer
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7
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https://www.w3.org/2000/01/rdf-schema#label
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Quadratic residues
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