{"id":2326,"date":"2022-05-27T13:19:43","date_gmt":"2022-05-27T16:19:43","guid":{"rendered":"https:\/\/icc.fcen.uba.ar\/?p=2326"},"modified":"2022-05-27T13:19:43","modified_gmt":"2022-05-27T16:19:43","slug":"on-a-question-of-mendes-france-on-normal-numbers","status":"publish","type":"post","link":"https:\/\/icc.fcen.uba.ar\/en\/on-a-question-of-mendes-france-on-normal-numbers\/","title":{"rendered":"On a question of Mend\u00e8s France on normal numbers"},"content":{"rendered":"<div class=\"fusion-fullwidth fullwidth-box fusion-builder-row-1 fusion-flex-container nonhundred-percent-fullwidth non-hundred-percent-height-scrolling\" style=\"--awb-border-radius-top-left:0px;--awb-border-radius-top-right:0px;--awb-border-radius-bottom-right:0px;--awb-border-radius-bottom-left:0px;--awb-flex-wrap:wrap;\" ><div class=\"fusion-builder-row fusion-row fusion-flex-align-items-flex-start fusion-flex-content-wrap\" style=\"max-width:1144px;margin-left: calc(-4% \/ 2 );margin-right: calc(-4% \/ 2 );\"><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-0 fusion_builder_column_1_1 1_1 fusion-flex-column\" style=\"--awb-bg-size:cover;--awb-width-large:100%;--awb-margin-top-large:0px;--awb-spacing-right-large:1.92%;--awb-margin-bottom-large:20px;--awb-spacing-left-large:1.92%;--awb-width-medium:100%;--awb-order-medium:0;--awb-spacing-right-medium:1.92%;--awb-spacing-left-medium:1.92%;--awb-width-small:100%;--awb-order-small:0;--awb-spacing-right-small:1.92%;--awb-spacing-left-small:1.92%;\"><div class=\"fusion-column-wrapper fusion-column-has-shadow fusion-flex-justify-content-flex-start fusion-content-layout-column\"><div class=\"fusion-text fusion-text-1\"><p>Authors: Ver\u00f3nica Becher, Manfred G. Madritsch.<\/p>\n<p>Abstract: In 2008 or earlier, Michel Mend\u00e8s France asked for an instance of a real number $x$ such that both $x$ and $1\/x$ are simply normal to a given integer base $b$. We give a positive answer to this question by constructing a number $x$ such that both $x$ and its reciprocal $1\/x$ are continued fraction normal as well as normal to all integer bases greater than or equal to $2$. Moreover, $x$ and $1\/x$ are both computable.<\/p>\n<p>More information:<\/p>\n<p><a href=\"https:\/\/www-2.dc.uba.ar\/staff\/becher\/papers\/x1x.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">https:\/\/www-2.dc.uba.ar\/staff\/becher\/papers\/x1x.pdf<\/a><\/p>\n<\/div><\/div><\/div><\/div><\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":9,"featured_media":2327,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[98],"tags":[],"class_list":["post-2326","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-papers"],"_links":{"self":[{"href":"https:\/\/icc.fcen.uba.ar\/en\/wp-json\/wp\/v2\/posts\/2326","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/icc.fcen.uba.ar\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/icc.fcen.uba.ar\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/icc.fcen.uba.ar\/en\/wp-json\/wp\/v2\/users\/9"}],"replies":[{"embeddable":true,"href":"https:\/\/icc.fcen.uba.ar\/en\/wp-json\/wp\/v2\/comments?post=2326"}],"version-history":[{"count":1,"href":"https:\/\/icc.fcen.uba.ar\/en\/wp-json\/wp\/v2\/posts\/2326\/revisions"}],"predecessor-version":[{"id":2328,"href":"https:\/\/icc.fcen.uba.ar\/en\/wp-json\/wp\/v2\/posts\/2326\/revisions\/2328"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/icc.fcen.uba.ar\/en\/wp-json\/wp\/v2\/media\/2327"}],"wp:attachment":[{"href":"https:\/\/icc.fcen.uba.ar\/en\/wp-json\/wp\/v2\/media?parent=2326"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/icc.fcen.uba.ar\/en\/wp-json\/wp\/v2\/categories?post=2326"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/icc.fcen.uba.ar\/en\/wp-json\/wp\/v2\/tags?post=2326"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}