{"id":50,"date":"2026-07-20T18:12:39","date_gmt":"2026-07-20T18:12:39","guid":{"rendered":"https:\/\/mathrelated.co.uk\/?page_id=50"},"modified":"2026-07-20T18:12:39","modified_gmt":"2026-07-20T18:12:39","slug":"relation-lowercase-g-in-group-1-12t2t1","status":"publish","type":"page","link":"https:\/\/mathrelated.co.uk\/index.php\/relation-lowercase-g-in-group-1-12t2t1\/","title":{"rendered":"Relation \u2018lowercase g\u2019 in group 1+(-1+2^t)*(2^(t+1))"},"content":{"rendered":"\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><mo>\u2212<\/mo><mn>1<\/mn><mo>+<\/mo><msup><mn>2<\/mn><mrow><mi>t<\/mi><mo>+<\/mo><mn>1<\/mn><\/mrow><\/msup><mo>\u2261<\/mo><mn>2<\/mn><mo>\u2217<\/mo><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>1<\/mn><mo>+<\/mo><msup><mn>2<\/mn><mrow><mn>2<\/mn><mo>\u2217<\/mo><mi>t<\/mi><\/mrow><\/msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">-1+2^{t+1}   \u2261   2*(1+2^{2*t})<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">For t=11 set N (composite)<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">\u00a04095<\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">For t=23 group P<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">\u00a016777215<\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">For t=39 group P<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">\u00a01099511627775<\/pre>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"782\" height=\"491\" src=\"https:\/\/mathrelated.co.uk\/wp-content\/uploads\/2026\/07\/lowercaseGrelationT11T23T39.jpeg\" alt=\"calculation of mod showing numeric output\" class=\"wp-image-63\" srcset=\"https:\/\/mathrelated.co.uk\/wp-content\/uploads\/2026\/07\/lowercaseGrelationT11T23T39.jpeg 782w, https:\/\/mathrelated.co.uk\/wp-content\/uploads\/2026\/07\/lowercaseGrelationT11T23T39-300x188.jpeg 300w, https:\/\/mathrelated.co.uk\/wp-content\/uploads\/2026\/07\/lowercaseGrelationT11T23T39-768x482.jpeg 768w\" sizes=\"auto, (max-width: 782px) 100vw, 782px\" \/><figcaption class=\"wp-element-caption\">lowercase &#8216;g&#8217; &#8211; showing identical<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>For t=11 set N (composite) \u00a04095 For t=23 group P \u00a016777215 For t=39 group P \u00a01099511627775<\/p>\n","protected":false},"author":1,"featured_media":51,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-50","page","type-page","status-publish","has-post-thumbnail","hentry"],"_links":{"self":[{"href":"https:\/\/mathrelated.co.uk\/index.php\/wp-json\/wp\/v2\/pages\/50","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathrelated.co.uk\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/mathrelated.co.uk\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/mathrelated.co.uk\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathrelated.co.uk\/index.php\/wp-json\/wp\/v2\/comments?post=50"}],"version-history":[{"count":1,"href":"https:\/\/mathrelated.co.uk\/index.php\/wp-json\/wp\/v2\/pages\/50\/revisions"}],"predecessor-version":[{"id":64,"href":"https:\/\/mathrelated.co.uk\/index.php\/wp-json\/wp\/v2\/pages\/50\/revisions\/64"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/mathrelated.co.uk\/index.php\/wp-json\/wp\/v2\/media\/51"}],"wp:attachment":[{"href":"https:\/\/mathrelated.co.uk\/index.php\/wp-json\/wp\/v2\/media?parent=50"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}