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Comptes Rendus. Mathématique
Théorie des nombres
On the continued fraction expansions of (1+pq)/2 and pq
Comptes Rendus. Mathématique, Tome 359 (2021) no. 9, pp. 1201-1205.

The evenness and the values modulo 4 of the lengths of the periods of the continued fraction expansions of p and 2p for p3(mod4) a prime are known. Here we prove similar results for the continued fraction expansion of pq, where p,q3(mod4) are distinct primes.

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DOI : https://doi.org/10.5802/crmath.266
Classification : 11A55,  11R11
@article{CRMATH_2021__359_9_1201_0,
     author = {St\'ephane R. Louboutin},
     title = {On the continued fraction expansions of $(1+\protect \sqrt{pq})/2$ and $\protect \sqrt{pq}$},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1201--1205},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {359},
     number = {9},
     year = {2021},
     doi = {10.5802/crmath.266},
     language = {en},
}
Stéphane R. Louboutin. On the continued fraction expansions of $(1+\protect \sqrt{pq})/2$ and $\protect \sqrt{pq}$. Comptes Rendus. Mathématique, Tome 359 (2021) no. 9, pp. 1201-1205. doi : 10.5802/crmath.266. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.266/

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