Although quadratic residues appear to occur in a rather random pattern modulo " n ", and this has been exploited in such cryptography, their distribution also exhibits some striking regularities.
42.
Also notice that if, then the congruence can be reduced to, but then this takes the problem away from quadratic residues ( unless " m " is a square ).
43.
Considering the nonzero elements of GF ( " p " ), it is a well-known fact that half of them are quadratic residues of " p ".
44.
This requires knowing whether " t " is a quadratic residue modulo " N ", and there are no known methods for doing this without knowledge of the factorisation.
45.
Chapters 2-4 of " A Pathway Into Number Theory " by R . P . Burn cover modular arithmetic and quadratic residues . talk ) 14 : 25, 14 May 2013 ( UTC)
46.
To test if 2 is a quadratic residue modulo 17, we calculate 2 ( 17 " 1 ) / 2 = 2 8 a " 1 ( mod 17 ), so it is a quadratic residue.
47.
To test if 2 is a quadratic residue modulo 17, we calculate 2 ( 17 " 1 ) / 2 = 2 8 a " 1 ( mod 17 ), so it is a quadratic residue.
48.
Determining whether " a " is a quadratic residue or nonresidue modulo " n " ( denoted or ) can be done efficiently for prime " n " by computing the Legendre symbol.
49.
Evaluating the square of the sum " P " is connected with the problem of counting how many quadratic residues between 1 and " p " & minus; 1 are succeeded by quadratic residues.
50.
Evaluating the square of the sum " P " is connected with the problem of counting how many quadratic residues between 1 and " p " & minus; 1 are succeeded by quadratic residues.
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