{"id":93,"date":"2026-07-20T20:31:13","date_gmt":"2026-07-20T20:31:13","guid":{"rendered":"https:\/\/mathrelated.co.uk\/?page_id=93"},"modified":"2026-07-20T20:31:13","modified_gmt":"2026-07-20T20:31:13","slug":"relation-lowercase-w-in-group-1-12t2t1","status":"publish","type":"page","link":"https:\/\/mathrelated.co.uk\/index.php\/relation-lowercase-w-in-group-1-12t2t1\/","title":{"rendered":"Relation \u2018lowercase w\u2019 in group 1+(-1+2^t)*(2^(t+1))"},"content":{"rendered":"\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><mn>2<\/mn><mo>\u2217<\/mo><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mo form=\"prefix\" stretchy=\"false\">\u2212<\/mo><mn>1<\/mn><mo>+<\/mo><msup><mn>2<\/mn><mrow><mi>t<\/mi><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>\u2261<\/mo><mo form=\"prefix\" stretchy=\"false\">\u2212<\/mo><mn>1<\/mn><mo>+<\/mo><msup><mn>2<\/mn><mrow><mn>1<\/mn><mo>+<\/mo><mn>3<\/mn><mo>\u2217<\/mo><mi>t<\/mi><\/mrow><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">2*(-1+2^{t-1})   \u2261   -1+2^{1+3*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\"> 2046<\/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\"> 8388606<\/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\"> 549755813886<\/pre>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"781\" height=\"490\" src=\"https:\/\/mathrelated.co.uk\/wp-content\/uploads\/2026\/07\/lowercaseWrelationT11T23T39.jpeg\" alt=\"calculation of mod showing numeric output\" class=\"wp-image-94\" srcset=\"https:\/\/mathrelated.co.uk\/wp-content\/uploads\/2026\/07\/lowercaseWrelationT11T23T39.jpeg 781w, https:\/\/mathrelated.co.uk\/wp-content\/uploads\/2026\/07\/lowercaseWrelationT11T23T39-300x188.jpeg 300w, https:\/\/mathrelated.co.uk\/wp-content\/uploads\/2026\/07\/lowercaseWrelationT11T23T39-768x482.jpeg 768w\" sizes=\"auto, (max-width: 781px) 100vw, 781px\" \/><figcaption class=\"wp-element-caption\">lowercase &#8216;w&#8217; &#8211; showing identical<\/figcaption><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>For t=11 set N (composite) 2046 For t=23 group P 8388606 For t=39 group P 549755813886<\/p>\n","protected":false},"author":1,"featured_media":61,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-93","page","type-page","status-publish","has-post-thumbnail","hentry"],"_links":{"self":[{"href":"https:\/\/mathrelated.co.uk\/index.php\/wp-json\/wp\/v2\/pages\/93","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=93"}],"version-history":[{"count":1,"href":"https:\/\/mathrelated.co.uk\/index.php\/wp-json\/wp\/v2\/pages\/93\/revisions"}],"predecessor-version":[{"id":95,"href":"https:\/\/mathrelated.co.uk\/index.php\/wp-json\/wp\/v2\/pages\/93\/revisions\/95"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/mathrelated.co.uk\/index.php\/wp-json\/wp\/v2\/media\/61"}],"wp:attachment":[{"href":"https:\/\/mathrelated.co.uk\/index.php\/wp-json\/wp\/v2\/media?parent=93"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}