{"id":74,"date":"2026-07-20T19:12:35","date_gmt":"2026-07-20T19:12:35","guid":{"rendered":"https:\/\/mathrelated.co.uk\/?page_id=74"},"modified":"2026-07-20T19:12:35","modified_gmt":"2026-07-20T19:12:35","slug":"relation-lowercase-p-in-group-1-12t2t1","status":"publish","type":"page","link":"https:\/\/mathrelated.co.uk\/index.php\/relation-lowercase-p-in-group-1-12t2t1\/","title":{"rendered":"Relation \u2018lowercase p\u2019 in group 1+(-1+2^t)*(2^(t+1))"},"content":{"rendered":"\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><msup><mn>2<\/mn><mrow><mn>3<\/mn><mo>+<\/mo><mn>3<\/mn><mo>\u2217<\/mo><mi>t<\/mi><\/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>1<\/mn><\/mrow><\/msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>\u2261<\/mo><msup><mn>2<\/mn><mrow><mn>1<\/mn><mo>+<\/mo><mn>2<\/mn><mo>\u2217<\/mo><mi>t<\/mi><\/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><mn>1<\/mn><mo>+<\/mo><mi>t<\/mi><mo>+<\/mo><mn>2<\/mn><mo>\u2217<\/mo><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>1<\/mn><mo>+<\/mo><mn>2<\/mn><mo>\u2217<\/mo><mi>t<\/mi><mo form=\"postfix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">)<\/mo><\/mrow><\/msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">2^{3+3*t}*(-1+2^{t-1})   \u2261   2^{1+2*t}*(-1+2^{1+t+2*(1+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\"> 8376324<\/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\"> 140737438023684<\/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\"> 604462909804016052469764<\/pre>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"784\" height=\"489\" src=\"https:\/\/mathrelated.co.uk\/wp-content\/uploads\/2026\/07\/lowercasePrelationT11T23T39.jpeg\" alt=\"calculation of mod showing numeric output\" class=\"wp-image-75\" srcset=\"https:\/\/mathrelated.co.uk\/wp-content\/uploads\/2026\/07\/lowercasePrelationT11T23T39.jpeg 784w, https:\/\/mathrelated.co.uk\/wp-content\/uploads\/2026\/07\/lowercasePrelationT11T23T39-300x187.jpeg 300w, https:\/\/mathrelated.co.uk\/wp-content\/uploads\/2026\/07\/lowercasePrelationT11T23T39-768x479.jpeg 768w\" sizes=\"auto, (max-width: 784px) 100vw, 784px\" \/><figcaption class=\"wp-element-caption\">lowercase &#8216;p&#8217; &#8211; showing identical<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>For t=11 set N (composite) 8376324 For t=23 group P 140737438023684 For t=39 group P 604462909804016052469764<\/p>\n","protected":false},"author":1,"featured_media":55,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-74","page","type-page","status-publish","has-post-thumbnail","hentry"],"_links":{"self":[{"href":"https:\/\/mathrelated.co.uk\/index.php\/wp-json\/wp\/v2\/pages\/74","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=74"}],"version-history":[{"count":1,"href":"https:\/\/mathrelated.co.uk\/index.php\/wp-json\/wp\/v2\/pages\/74\/revisions"}],"predecessor-version":[{"id":76,"href":"https:\/\/mathrelated.co.uk\/index.php\/wp-json\/wp\/v2\/pages\/74\/revisions\/76"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/mathrelated.co.uk\/index.php\/wp-json\/wp\/v2\/media\/55"}],"wp:attachment":[{"href":"https:\/\/mathrelated.co.uk\/index.php\/wp-json\/wp\/v2\/media?parent=74"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}