The evenness and the values modulo of the lengths of the periods of the continued fraction expansions of and for a prime are known. Here we prove similar results for the continued fraction expansion of , where are distinct primes.
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Stéphane R. Louboutin 1
@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}, }
TY - JOUR AU - Stéphane R. Louboutin TI - On the continued fraction expansions of $(1+\protect \sqrt{pq})/2$ and $\protect \sqrt{pq}$ JO - Comptes Rendus. Mathématique PY - 2021 SP - 1201 EP - 1205 VL - 359 IS - 9 PB - Académie des sciences, Paris DO - 10.5802/crmath.266 LA - en ID - CRMATH_2021__359_9_1201_0 ER -
Stéphane R. Louboutin. On the continued fraction expansions of $(1+\protect \sqrt{pq})/2$ and $\protect \sqrt{pq}$. Comptes Rendus. Mathématique, Volume 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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