{"id":38,"date":"2026-07-20T16:22:07","date_gmt":"2026-07-20T16:22:07","guid":{"rendered":"https:\/\/mathrelated.co.uk\/?page_id=38"},"modified":"2026-07-20T16:23:26","modified_gmt":"2026-07-20T16:23:26","slug":"relation-lowercase-d-in-group-1-12t2t1","status":"publish","type":"page","link":"https:\/\/mathrelated.co.uk\/index.php\/relation-lowercase-d-in-group-1-12t2t1\/","title":{"rendered":"Relation &#8216;lowercase d&#8217; 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><msup><mn>2<\/mn><mrow><mi>t<\/mi><mo>+<\/mo><mn>2<\/mn><\/mrow><\/msup><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>2<\/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><mi>t<\/mi><\/msup><msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">-2^{t+2}*(-1+2^{t-2})   \u2261   (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\">&nbsp;4198401<\/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\">&nbsp;70368760954881<\/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\">&nbsp;302231454904756805304321<\/pre>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"885\" height=\"487\" src=\"https:\/\/mathrelated.co.uk\/wp-content\/uploads\/2026\/07\/lowercaseDrelationT11T23T39.jpeg\" alt=\"calculation of mod showing numeric results\" class=\"wp-image-40\" srcset=\"https:\/\/mathrelated.co.uk\/wp-content\/uploads\/2026\/07\/lowercaseDrelationT11T23T39.jpeg 885w, https:\/\/mathrelated.co.uk\/wp-content\/uploads\/2026\/07\/lowercaseDrelationT11T23T39-300x165.jpeg 300w, https:\/\/mathrelated.co.uk\/wp-content\/uploads\/2026\/07\/lowercaseDrelationT11T23T39-768x423.jpeg 768w\" sizes=\"auto, (max-width: 885px) 100vw, 885px\" \/><figcaption class=\"wp-element-caption\">lowercase &#8216;d&#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) &nbsp;4198401 For t=23 group P &nbsp;70368760954881 For t=39 group P &nbsp;302231454904756805304321<\/p>\n","protected":false},"author":1,"featured_media":39,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-38","page","type-page","status-publish","has-post-thumbnail","hentry"],"_links":{"self":[{"href":"https:\/\/mathrelated.co.uk\/index.php\/wp-json\/wp\/v2\/pages\/38","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=38"}],"version-history":[{"count":2,"href":"https:\/\/mathrelated.co.uk\/index.php\/wp-json\/wp\/v2\/pages\/38\/revisions"}],"predecessor-version":[{"id":42,"href":"https:\/\/mathrelated.co.uk\/index.php\/wp-json\/wp\/v2\/pages\/38\/revisions\/42"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/mathrelated.co.uk\/index.php\/wp-json\/wp\/v2\/media\/39"}],"wp:attachment":[{"href":"https:\/\/mathrelated.co.uk\/index.php\/wp-json\/wp\/v2\/media?parent=38"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}