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Gauss published the first and second proofs of the law of quadratic reciprocity on arts 125–146 and 262 of Disquisitiones Arithmeticae in 1801.. In number theory, the law of quadratic reciprocity is a theorem about modular arithmetic that gives conditions for the solvability of quadratic equations modulo prime numbers.
Lemmermeyer, Franz (2000), Reciprocity Laws: from Euler to Eisenstein, Springer Monographs in Mathematics, Berlin: Springer, ISBN 3-540-66957-4 Rousseau, G. (1991), "On the Quadratic Reciprocity Law" , Journal of the Australian Mathematical Society, Series A , 51 , Cambridge University Press: 423– 425, ISSN 1446-7887
In another case, testing p = 13, we have 17 (13 − 1)/2 = 17 6 ≡ 1 (mod 13), therefore 17 is a quadratic residue modulo 13. As confirmation, note that 17 ≡ 4 (mod 13), and 2 2 = 4. We can do these calculations faster by using various modular arithmetic and Legendre symbol properties. If we keep calculating the values, we find:
Questions on the NCLEX exam are of three different types or levels: Level 1, Level 2, and Level 3. Level 1 questions are the most basic questions and make up less than 10 percent of the total questions. Level 1 questions test the individual's knowledge and understanding. These questions require the individual to recall specific facts and ...
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c ≡ 4 13 (mod 497) One could use a calculator to compute 4 13; this comes out to 67,108,864. ... In practice, we would usually want the result modulo some modulus m.