{"id":164,"date":"2026-07-26T21:02:34","date_gmt":"2026-07-26T15:32:34","guid":{"rendered":"https:\/\/deepwrites.com\/?p=164"},"modified":"2026-07-26T21:04:17","modified_gmt":"2026-07-26T15:34:17","slug":"on-the-dimension-of-solution-spaces-and-a-characterization-of-primes-in-group-theoretic-identity","status":"publish","type":"post","link":"https:\/\/deepwrites.com\/?p=164","title":{"rendered":"On the Dimension of Solution Spaces and a Characterization of primes in Group-Theoretic Identity."},"content":{"rendered":"\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>Welcome to my collection of mathematical articles. Here I publish notes, proofs, and expository pieces on topics that interest me, particularly in analysis, differential equations, algebra, and theoritical computer science. New articles will be added as I continue my studies and attempt my hand at solving the unsolved.<\/p>\n<\/blockquote>\n\n\n\n<h3 class=\"wp-block-heading\">This article presents the following proofs:<\/h3>\n\n\n\n<p><strong>1. On the Solution Space of an n-th Order Linear Homogeneous Differential Equation<\/strong><br>A proof showing that the solution space of an n-th order linear homogeneous differential equation is an n-dimensional vector space: <a href=\"https:\/\/deepwrites.com\/dimension-of-solution-space.html\">https:\/\/deepwrites.com\/dimension-of-solution-space.html<\/a><\/p>\n\n\n\n<p><strong>2. Characterization and Analysis of a Problem from the Open Problem Garden with Connections to Finite Group Theory<\/strong><br>A note on higher power residues modulo primes, including the case p=2, together with connections to finite group theory: <a href=\"https:\/\/yourdomain.com\/dimension-of-solution-space.html\">https:\/\/deepwrites.com\/Characterization-of-primes.html<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Welcome to my collection of mathematical articles. Here I publish notes, proofs, and expository pieces on topics that<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"image","meta":{"footnotes":""},"categories":[1],"tags":[],"_links":{"self":[{"href":"https:\/\/deepwrites.com\/index.php?rest_route=\/wp\/v2\/posts\/164"}],"collection":[{"href":"https:\/\/deepwrites.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/deepwrites.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/deepwrites.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/deepwrites.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=164"}],"version-history":[{"count":5,"href":"https:\/\/deepwrites.com\/index.php?rest_route=\/wp\/v2\/posts\/164\/revisions"}],"predecessor-version":[{"id":169,"href":"https:\/\/deepwrites.com\/index.php?rest_route=\/wp\/v2\/posts\/164\/revisions\/169"}],"wp:attachment":[{"href":"https:\/\/deepwrites.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=164"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/deepwrites.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=164"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/deepwrites.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=164"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}