Geodesic
On the Quadratic Residues (Mod p) in the Interval (0, p/4)
Canadian mathematical bulletin, Tome 26 (1983) no. 1, pp. 123-124

Voir la notice de l'article provenant de la source Cambridge University Press

A short proof is given of a result of Burde giving the parity of the number of quadratic residues (mod p) in the interval (0, p/4), where p ≡ 1(mod 4) is prime.
DOI : 10.4153/CMB-1983-020-5
Mots-clés : 10A15, Secondary 10E15, 12H50, 12H25 
Williams, Kenneth S. On the Quadratic Residues (Mod p) in the Interval (0, p/4). Canadian mathematical bulletin, Tome 26 (1983) no. 1, pp. 123-124. doi: 10.4153/CMB-1983-020-5
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[1] 1. Barkan, Philippe, Une propriété de congruence de la longueur de la période d'un développement en fraction continue, C.R. Acad. Se. Paris 281 (1975), 825-828. Google Scholar

[2] 2. Burde, Klaus, Eine Verteilungseigenschaft der Legendresymbole, J. Number Theory 12 (1980), 273-277. Google Scholar

[3] 3. Dickson, L. E., History of the Theory of Numbers, Volume 3, reprinted Chelsea Publishing Company, Bronx, N.Y. (1966). Google Scholar

[4] 4. Dirichlet, P. G. L., Recherches sur diverses applications de l'analyse infinitésimale ? la théorie des nombres, J. Reine Angew. Math. 21 (1840), 134-155. Google Scholar

[5] 5. Gauss, Cari Friedrich, Letter to P. G. L. Dirichlet dated 30 May 1828. (Reproduced in G. Lejeune Dirichlet's Werke, Chelsea Publishing Company, Bronx, N.Y. (1969) Volume 2, pp. 378-380.) Google Scholar

[6] 6. Yamamoto, Koichi, On Gaussian sums with biquadratic residue characters, J. Reine Angew. Math. 219 (1965), 200-213. Google Scholar

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