{"id":105,"date":"2026-07-27T16:16:39","date_gmt":"2026-07-27T16:16:39","guid":{"rendered":"https:\/\/mathrelated.co.uk\/?p=105"},"modified":"2026-08-14T19:36:35","modified_gmt":"2026-08-14T19:36:35","slug":"abundant-relations-in-1-12t2t1","status":"publish","type":"post","link":"https:\/\/mathrelated.co.uk\/index.php\/2026\/07\/27\/abundant-relations-in-1-12t2t1\/","title":{"rendered":"Abundant relations in 1+(-1+2^t)*(2^(t+1))"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">The  number space <\/p>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><mn>1<\/mn><mo>+<\/mo><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mo form=\"prefix\" stretchy=\"false\">\u2212<\/mo><mn>1<\/mn><mo>+<\/mo><msup><mn>2<\/mn><mi>t<\/mi><\/msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>\u2217<\/mo><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msup><mn>2<\/mn><mrow><mi>t<\/mi><mo>+<\/mo><mn>1<\/mn><\/mrow><\/msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">1+(-1+2^t)*(2^{t+1})<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">has an abundance of relations<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In this post I provide links to pages about those relations<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-wp-embed is-provider-mathrelated wp-block-embed-mathrelated\"><div class=\"wp-block-embed__wrapper\">\n<blockquote class=\"wp-embedded-content\" data-secret=\"aCizOfynY0\"><a href=\"https:\/\/mathrelated.co.uk\/index.php\/relation-lowercase-b-in-group-1-12t2t1\/\">Relation &#8216;lowercase b&#8217; in group 1+(-1+2^t)*(2^(t+1))<\/a><\/blockquote><iframe loading=\"lazy\" class=\"wp-embedded-content\" sandbox=\"allow-scripts\" security=\"restricted\" style=\"position: absolute; visibility: hidden;\" title=\"\u201cRelation \u2018lowercase b\u2019 in group 1+(-1+2^t)*(2^(t+1))\u201d \u2014 Mathrelated\" src=\"https:\/\/mathrelated.co.uk\/index.php\/relation-lowercase-b-in-group-1-12t2t1\/embed\/#?secret=YstS1tdELK#?secret=aCizOfynY0\" data-secret=\"aCizOfynY0\" width=\"500\" height=\"282\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\"><\/iframe>\n<\/div><\/figure>\n\n\n\n<figure class=\"wp-block-embed is-type-wp-embed is-provider-mathrelated wp-block-embed-mathrelated\"><div class=\"wp-block-embed__wrapper\">\n<blockquote class=\"wp-embedded-content\" data-secret=\"RNyg31LVXV\"><a href=\"https:\/\/mathrelated.co.uk\/index.php\/relation-lowercase-c-in-group-1-12t2t1\/\">Relation &#8216;lowercase c&#8217; in group 1+(-1+2^t)*(2^(t+1))<\/a><\/blockquote><iframe loading=\"lazy\" class=\"wp-embedded-content\" sandbox=\"allow-scripts\" security=\"restricted\" style=\"position: absolute; visibility: hidden;\" title=\"\u201cRelation \u2018lowercase c\u2019 in group 1+(-1+2^t)*(2^(t+1))\u201d \u2014 Mathrelated\" src=\"https:\/\/mathrelated.co.uk\/index.php\/relation-lowercase-c-in-group-1-12t2t1\/embed\/#?secret=84PIvmxUYJ#?secret=RNyg31LVXV\" data-secret=\"RNyg31LVXV\" width=\"500\" height=\"282\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\"><\/iframe>\n<\/div><\/figure>\n\n\n\n<figure class=\"wp-block-embed is-type-wp-embed is-provider-mathrelated wp-block-embed-mathrelated\"><div class=\"wp-block-embed__wrapper\">\n<blockquote class=\"wp-embedded-content\" data-secret=\"iK5j25xP8S\"><a href=\"https:\/\/mathrelated.co.uk\/index.php\/relation-lowercase-d-in-group-1-12t2t1\/\">Relation &#8216;lowercase d&#8217; in group 1+(-1+2^t)*(2^(t+1))<\/a><\/blockquote><iframe loading=\"lazy\" class=\"wp-embedded-content\" sandbox=\"allow-scripts\" security=\"restricted\" style=\"position: absolute; visibility: hidden;\" title=\"\u201cRelation \u2018lowercase d\u2019 in group 1+(-1+2^t)*(2^(t+1))\u201d \u2014 Mathrelated\" src=\"https:\/\/mathrelated.co.uk\/index.php\/relation-lowercase-d-in-group-1-12t2t1\/embed\/#?secret=iK50FqAnmX#?secret=iK5j25xP8S\" data-secret=\"iK5j25xP8S\" width=\"500\" height=\"282\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\"><\/iframe>\n<\/div><\/figure>\n\n\n\n<figure class=\"wp-block-embed is-type-wp-embed is-provider-mathrelated wp-block-embed-mathrelated\"><div class=\"wp-block-embed__wrapper\">\n<blockquote class=\"wp-embedded-content\" data-secret=\"JG3voeIAX0\"><a href=\"https:\/\/mathrelated.co.uk\/index.php\/relation-lowercase-f-in-group-1-12t2t1\/\">Relation \u2018lowercase f\u2019 in group 1+(-1+2^t)*(2^(t+1))<\/a><\/blockquote><iframe loading=\"lazy\" class=\"wp-embedded-content\" sandbox=\"allow-scripts\" security=\"restricted\" style=\"position: absolute; visibility: hidden;\" title=\"\u201cRelation \u2018lowercase f\u2019 in group 1+(-1+2^t)*(2^(t+1))\u201d \u2014 Mathrelated\" src=\"https:\/\/mathrelated.co.uk\/index.php\/relation-lowercase-f-in-group-1-12t2t1\/embed\/#?secret=BNhvKXRe3e#?secret=JG3voeIAX0\" data-secret=\"JG3voeIAX0\" width=\"500\" height=\"282\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\"><\/iframe>\n<\/div><\/figure>\n\n\n\n<figure class=\"wp-block-embed is-type-wp-embed is-provider-mathrelated wp-block-embed-mathrelated\"><div class=\"wp-block-embed__wrapper\">\n<blockquote class=\"wp-embedded-content\" data-secret=\"htgVhTi9tD\"><a href=\"https:\/\/mathrelated.co.uk\/index.php\/relation-lowercase-g-in-group-1-12t2t1\/\">Relation \u2018lowercase g\u2019 in group 1+(-1+2^t)*(2^(t+1))<\/a><\/blockquote><iframe loading=\"lazy\" class=\"wp-embedded-content\" sandbox=\"allow-scripts\" security=\"restricted\" style=\"position: absolute; visibility: hidden;\" title=\"\u201cRelation \u2018lowercase g\u2019 in group 1+(-1+2^t)*(2^(t+1))\u201d \u2014 Mathrelated\" src=\"https:\/\/mathrelated.co.uk\/index.php\/relation-lowercase-g-in-group-1-12t2t1\/embed\/#?secret=S05Mkxd5hU#?secret=htgVhTi9tD\" data-secret=\"htgVhTi9tD\" width=\"500\" height=\"282\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\"><\/iframe>\n<\/div><\/figure>\n\n\n\n<figure class=\"wp-block-embed is-type-wp-embed is-provider-mathrelated wp-block-embed-mathrelated\"><div class=\"wp-block-embed__wrapper\">\n<blockquote class=\"wp-embedded-content\" data-secret=\"mxAoXAFb5z\"><a href=\"https:\/\/mathrelated.co.uk\/index.php\/relation-lowercase-h-in-group-1-12t2t1\/\">Relation \u2018lowercase h\u2019 in group 1+(-1+2^t)*(2^(t+1))<\/a><\/blockquote><iframe loading=\"lazy\" class=\"wp-embedded-content\" sandbox=\"allow-scripts\" security=\"restricted\" style=\"position: absolute; visibility: hidden;\" title=\"\u201cRelation \u2018lowercase h\u2019 in group 1+(-1+2^t)*(2^(t+1))\u201d \u2014 Mathrelated\" src=\"https:\/\/mathrelated.co.uk\/index.php\/relation-lowercase-h-in-group-1-12t2t1\/embed\/#?secret=ogKRiXuLTB#?secret=mxAoXAFb5z\" data-secret=\"mxAoXAFb5z\" width=\"500\" height=\"282\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\"><\/iframe>\n<\/div><\/figure>\n\n\n\n<figure class=\"wp-block-embed is-type-wp-embed is-provider-mathrelated wp-block-embed-mathrelated\"><div class=\"wp-block-embed__wrapper\">\n<blockquote class=\"wp-embedded-content\" data-secret=\"YOKxDFjjR8\"><a href=\"https:\/\/mathrelated.co.uk\/index.php\/relation-lowercase-i-in-group-1-12t2t1\/\">Relation \u2018lowercase i\u2019 in group 1+(-1+2^t)*(2^(t+1))<\/a><\/blockquote><iframe loading=\"lazy\" class=\"wp-embedded-content\" sandbox=\"allow-scripts\" security=\"restricted\" style=\"position: absolute; visibility: hidden;\" title=\"\u201cRelation \u2018lowercase i\u2019 in group 1+(-1+2^t)*(2^(t+1))\u201d \u2014 Mathrelated\" src=\"https:\/\/mathrelated.co.uk\/index.php\/relation-lowercase-i-in-group-1-12t2t1\/embed\/#?secret=9wZPyQJI19#?secret=YOKxDFjjR8\" data-secret=\"YOKxDFjjR8\" width=\"500\" height=\"282\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\"><\/iframe>\n<\/div><\/figure>\n\n\n\n<figure class=\"wp-block-embed is-type-wp-embed is-provider-mathrelated wp-block-embed-mathrelated\"><div class=\"wp-block-embed__wrapper\">\n<blockquote class=\"wp-embedded-content\" data-secret=\"0WZvzTAQpB\"><a href=\"https:\/\/mathrelated.co.uk\/index.php\/relation-lowercase-n-in-group-1-12t2t1\/\">Relation \u2018lowercase n\u2019 in group 1+(-1+2^t)*(2^(t+1))<\/a><\/blockquote><iframe loading=\"lazy\" class=\"wp-embedded-content\" sandbox=\"allow-scripts\" security=\"restricted\" style=\"position: absolute; visibility: hidden;\" title=\"\u201cRelation \u2018lowercase n\u2019 in group 1+(-1+2^t)*(2^(t+1))\u201d \u2014 Mathrelated\" src=\"https:\/\/mathrelated.co.uk\/index.php\/relation-lowercase-n-in-group-1-12t2t1\/embed\/#?secret=xqdNK6Ln3q#?secret=0WZvzTAQpB\" data-secret=\"0WZvzTAQpB\" width=\"500\" height=\"282\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\"><\/iframe>\n<\/div><\/figure>\n\n\n\n<figure class=\"wp-block-embed is-type-wp-embed is-provider-mathrelated wp-block-embed-mathrelated\"><div class=\"wp-block-embed__wrapper\">\n<blockquote class=\"wp-embedded-content\" data-secret=\"TRZK4WzGT5\"><a href=\"https:\/\/mathrelated.co.uk\/index.php\/relation-lowercase-p-in-group-1-12t2t1\/\">Relation \u2018lowercase p\u2019 in group 1+(-1+2^t)*(2^(t+1))<\/a><\/blockquote><iframe loading=\"lazy\" class=\"wp-embedded-content\" sandbox=\"allow-scripts\" security=\"restricted\" style=\"position: absolute; visibility: hidden;\" title=\"\u201cRelation \u2018lowercase p\u2019 in group 1+(-1+2^t)*(2^(t+1))\u201d \u2014 Mathrelated\" src=\"https:\/\/mathrelated.co.uk\/index.php\/relation-lowercase-p-in-group-1-12t2t1\/embed\/#?secret=CZ8W0IjYtT#?secret=TRZK4WzGT5\" data-secret=\"TRZK4WzGT5\" width=\"500\" height=\"282\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\"><\/iframe>\n<\/div><\/figure>\n\n\n\n<figure class=\"wp-block-embed is-type-wp-embed is-provider-mathrelated wp-block-embed-mathrelated\"><div class=\"wp-block-embed__wrapper\">\n<blockquote class=\"wp-embedded-content\" data-secret=\"zRKsu9SIuz\"><a href=\"https:\/\/mathrelated.co.uk\/index.php\/relation-lowercase-q-in-group-1-12t2t1\/\">Relation \u2018lowercase q\u2019 in group 1+(-1+2^t)*(2^(t+1))<\/a><\/blockquote><iframe loading=\"lazy\" class=\"wp-embedded-content\" sandbox=\"allow-scripts\" security=\"restricted\" style=\"position: absolute; visibility: hidden;\" title=\"\u201cRelation \u2018lowercase q\u2019 in group 1+(-1+2^t)*(2^(t+1))\u201d \u2014 Mathrelated\" src=\"https:\/\/mathrelated.co.uk\/index.php\/relation-lowercase-q-in-group-1-12t2t1\/embed\/#?secret=L0EBkCFpuB#?secret=zRKsu9SIuz\" data-secret=\"zRKsu9SIuz\" width=\"500\" height=\"282\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\"><\/iframe>\n<\/div><\/figure>\n\n\n\n<figure class=\"wp-block-embed is-type-wp-embed is-provider-mathrelated wp-block-embed-mathrelated\"><div class=\"wp-block-embed__wrapper\">\n<blockquote class=\"wp-embedded-content\" data-secret=\"KaDekLeCZ2\"><a href=\"https:\/\/mathrelated.co.uk\/index.php\/relation-lowercase-r-in-group-1-12t2t1\/\">Relation \u2018lowercase r\u2019 in group 1+(-1+2^t)*(2^(t+1))<\/a><\/blockquote><iframe loading=\"lazy\" class=\"wp-embedded-content\" sandbox=\"allow-scripts\" security=\"restricted\" style=\"position: absolute; visibility: hidden;\" title=\"\u201cRelation \u2018lowercase r\u2019 in group 1+(-1+2^t)*(2^(t+1))\u201d \u2014 Mathrelated\" src=\"https:\/\/mathrelated.co.uk\/index.php\/relation-lowercase-r-in-group-1-12t2t1\/embed\/#?secret=eN2p1Jta9K#?secret=KaDekLeCZ2\" data-secret=\"KaDekLeCZ2\" width=\"500\" height=\"282\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\"><\/iframe>\n<\/div><\/figure>\n\n\n\n<figure class=\"wp-block-embed is-type-wp-embed is-provider-mathrelated wp-block-embed-mathrelated\"><div class=\"wp-block-embed__wrapper\">\n<blockquote class=\"wp-embedded-content\" data-secret=\"LLSEBNZQIS\"><a href=\"https:\/\/mathrelated.co.uk\/index.php\/relation-lowercase-s-in-group-1-12t2t1\/\">Relation \u2018lowercase s\u2019 in group 1+(-1+2^t)*(2^(t+1))<\/a><\/blockquote><iframe loading=\"lazy\" class=\"wp-embedded-content\" sandbox=\"allow-scripts\" security=\"restricted\" style=\"position: absolute; visibility: hidden;\" title=\"\u201cRelation \u2018lowercase s\u2019 in group 1+(-1+2^t)*(2^(t+1))\u201d \u2014 Mathrelated\" src=\"https:\/\/mathrelated.co.uk\/index.php\/relation-lowercase-s-in-group-1-12t2t1\/embed\/#?secret=MDgyPrDlwy#?secret=LLSEBNZQIS\" data-secret=\"LLSEBNZQIS\" width=\"500\" height=\"282\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\"><\/iframe>\n<\/div><\/figure>\n\n\n\n<figure class=\"wp-block-embed is-type-wp-embed is-provider-mathrelated wp-block-embed-mathrelated\"><div class=\"wp-block-embed__wrapper\">\n<blockquote class=\"wp-embedded-content\" data-secret=\"rZwfaPkM6l\"><a href=\"https:\/\/mathrelated.co.uk\/index.php\/relation-lowercase-t-in-group-1-12t2t1\/\">Relation \u2018lowercase t\u2019 in group 1+(-1+2^t)*(2^(t+1))<\/a><\/blockquote><iframe loading=\"lazy\" class=\"wp-embedded-content\" sandbox=\"allow-scripts\" security=\"restricted\" style=\"position: absolute; visibility: hidden;\" title=\"\u201cRelation \u2018lowercase t\u2019 in group 1+(-1+2^t)*(2^(t+1))\u201d \u2014 Mathrelated\" src=\"https:\/\/mathrelated.co.uk\/index.php\/relation-lowercase-t-in-group-1-12t2t1\/embed\/#?secret=1Od21pkPkj#?secret=rZwfaPkM6l\" data-secret=\"rZwfaPkM6l\" width=\"500\" height=\"282\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\"><\/iframe>\n<\/div><\/figure>\n\n\n\n<figure class=\"wp-block-embed is-type-wp-embed is-provider-mathrelated wp-block-embed-mathrelated\"><div class=\"wp-block-embed__wrapper\">\n<blockquote class=\"wp-embedded-content\" data-secret=\"qJcnAUHg14\"><a href=\"https:\/\/mathrelated.co.uk\/index.php\/relation-lowercase-u-in-group-1-12t2t1\/\">Relation \u2018lowercase u\u2019 in group 1+(-1+2^t)*(2^(t+1))<\/a><\/blockquote><iframe loading=\"lazy\" class=\"wp-embedded-content\" sandbox=\"allow-scripts\" security=\"restricted\" style=\"position: absolute; visibility: hidden;\" title=\"\u201cRelation \u2018lowercase u\u2019 in group 1+(-1+2^t)*(2^(t+1))\u201d \u2014 Mathrelated\" src=\"https:\/\/mathrelated.co.uk\/index.php\/relation-lowercase-u-in-group-1-12t2t1\/embed\/#?secret=5VkzbOHExL#?secret=qJcnAUHg14\" data-secret=\"qJcnAUHg14\" width=\"500\" height=\"282\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\"><\/iframe>\n<\/div><\/figure>\n\n\n\n<figure class=\"wp-block-embed is-type-wp-embed is-provider-mathrelated wp-block-embed-mathrelated\"><div class=\"wp-block-embed__wrapper\">\n<blockquote class=\"wp-embedded-content\" data-secret=\"VeYzYTc5bs\"><a href=\"https:\/\/mathrelated.co.uk\/index.php\/relation-lowercase-w-in-group-1-12t2t1\/\">Relation \u2018lowercase w\u2019 in group 1+(-1+2^t)*(2^(t+1))<\/a><\/blockquote><iframe loading=\"lazy\" class=\"wp-embedded-content\" sandbox=\"allow-scripts\" security=\"restricted\" style=\"position: absolute; visibility: hidden;\" title=\"\u201cRelation \u2018lowercase w\u2019 in group 1+(-1+2^t)*(2^(t+1))\u201d \u2014 Mathrelated\" src=\"https:\/\/mathrelated.co.uk\/index.php\/relation-lowercase-w-in-group-1-12t2t1\/embed\/#?secret=2QMvWs7ONJ#?secret=VeYzYTc5bs\" data-secret=\"VeYzYTc5bs\" width=\"500\" height=\"282\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\"><\/iframe>\n<\/div><\/figure>\n\n\n\n<figure class=\"wp-block-embed is-type-wp-embed is-provider-mathrelated wp-block-embed-mathrelated\"><div class=\"wp-block-embed__wrapper\">\n<blockquote class=\"wp-embedded-content\" data-secret=\"zeyeCx5YCK\"><a href=\"https:\/\/mathrelated.co.uk\/index.php\/relation-lowercase-z-in-group-1-12t2t1\/\">Relation \u2018lowercase z\u2019 in group 1+(-1+2^t)*(2^(t+1))<\/a><\/blockquote><iframe loading=\"lazy\" class=\"wp-embedded-content\" sandbox=\"allow-scripts\" security=\"restricted\" style=\"position: absolute; visibility: hidden;\" title=\"\u201cRelation \u2018lowercase z\u2019 in group 1+(-1+2^t)*(2^(t+1))\u201d \u2014 Mathrelated\" src=\"https:\/\/mathrelated.co.uk\/index.php\/relation-lowercase-z-in-group-1-12t2t1\/embed\/#?secret=NcxW6q5Owk#?secret=zeyeCx5YCK\" data-secret=\"zeyeCx5YCK\" width=\"500\" height=\"282\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\"><\/iframe>\n<\/div><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Relations in 1+(-1+2^t)*(2^(t+1)) are abundant. Links to relations b,c,d,f,g,h,i,n,p,q,r,s,t,u,w,z are provided.<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5,6],"tags":[9,10],"class_list":["post-105","post","type-post","status-publish","format-standard","hentry","category-mathematics","category-numbertheory","tag-congruence","tag-relation"],"_links":{"self":[{"href":"https:\/\/mathrelated.co.uk\/index.php\/wp-json\/wp\/v2\/posts\/105","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathrelated.co.uk\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathrelated.co.uk\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathrelated.co.uk\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/mathrelated.co.uk\/index.php\/wp-json\/wp\/v2\/comments?post=105"}],"version-history":[{"count":1,"href":"https:\/\/mathrelated.co.uk\/index.php\/wp-json\/wp\/v2\/posts\/105\/revisions"}],"predecessor-version":[{"id":106,"href":"https:\/\/mathrelated.co.uk\/index.php\/wp-json\/wp\/v2\/posts\/105\/revisions\/106"}],"wp:attachment":[{"href":"https:\/\/mathrelated.co.uk\/index.php\/wp-json\/wp\/v2\/media?parent=105"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathrelated.co.uk\/index.php\/wp-json\/wp\/v2\/categories?post=105"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathrelated.co.uk\/index.php\/wp-json\/wp\/v2\/tags?post=105"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}