{"id":25,"date":"2026-07-20T15:50:44","date_gmt":"2026-07-20T15:50:44","guid":{"rendered":"https:\/\/mathrelated.co.uk\/?page_id=25"},"modified":"2026-07-20T15:50:44","modified_gmt":"2026-07-20T15:50:44","slug":"relation-lowercase-b-in-group-1-12t2t1","status":"publish","type":"page","link":"https:\/\/mathrelated.co.uk\/index.php\/relation-lowercase-b-in-group-1-12t2t1\/","title":{"rendered":"Relation &#8216;lowercase b&#8217; in group 1+(-1+2^t)*(2^(t+1))"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\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>+<\/mo><mn>1<\/mn><\/mrow><\/msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>\u2261<\/mo><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>1<\/mn><mo>+<\/mo><msup><mn>2<\/mn><mrow><mn>1<\/mn><mo>+<\/mo><mn>2<\/mn><mo>\u2217<\/mo><mi>t<\/mi><\/mrow><\/msup><msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">2*(-1+2^{t+1}) \u2261 (1+2^{1+2*t})^2<\/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\"> 8190<\/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\"> 33554430<\/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\"> 2199023255550<\/pre>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"888\" height=\"491\" src=\"https:\/\/mathrelated.co.uk\/wp-content\/uploads\/2026\/07\/lowercaseBrelationT11T23T39.jpeg\" alt=\"calculations of mod with numeric results\" class=\"wp-image-22\" srcset=\"https:\/\/mathrelated.co.uk\/wp-content\/uploads\/2026\/07\/lowercaseBrelationT11T23T39.jpeg 888w, https:\/\/mathrelated.co.uk\/wp-content\/uploads\/2026\/07\/lowercaseBrelationT11T23T39-300x166.jpeg 300w, https:\/\/mathrelated.co.uk\/wp-content\/uploads\/2026\/07\/lowercaseBrelationT11T23T39-768x425.jpeg 768w\" sizes=\"auto, (max-width: 888px) 100vw, 888px\" \/><figcaption class=\"wp-element-caption\">lowercase &#8216;b&#8217; &#8211; showing identical<\/figcaption><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>For t=11 set N (composite) 8190 For t=23 group P 33554430 For t=39 group P 2199023255550<\/p>\n","protected":false},"author":1,"featured_media":27,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-25","page","type-page","status-publish","has-post-thumbnail","hentry"],"_links":{"self":[{"href":"https:\/\/mathrelated.co.uk\/index.php\/wp-json\/wp\/v2\/pages\/25","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=25"}],"version-history":[{"count":2,"href":"https:\/\/mathrelated.co.uk\/index.php\/wp-json\/wp\/v2\/pages\/25\/revisions"}],"predecessor-version":[{"id":28,"href":"https:\/\/mathrelated.co.uk\/index.php\/wp-json\/wp\/v2\/pages\/25\/revisions\/28"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/mathrelated.co.uk\/index.php\/wp-json\/wp\/v2\/media\/27"}],"wp:attachment":[{"href":"https:\/\/mathrelated.co.uk\/index.php\/wp-json\/wp\/v2\/media?parent=25"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}