{"id":494,"date":"2020-05-31T22:18:48","date_gmt":"2020-05-31T22:18:48","guid":{"rendered":"http:\/\/blog.newtonchineseschool.org\/lilijia\/?p=494"},"modified":"2020-05-31T22:18:48","modified_gmt":"2020-05-31T22:18:48","slug":"aops-number-theory-ch-14i-linear-congruences","status":"publish","type":"post","link":"https:\/\/blog.newtonchineseschool.org\/lilijia\/2020\/05\/31\/aops-number-theory-ch-14i-linear-congruences\/","title":{"rendered":"AoPS Number Theory Ch.14(I) Linear Congruences"},"content":{"rendered":"\n<p>Sorry about the technical issue that I could not connect my iPad to Zoom in class today. Later on, I downloaded the newest version of Zoom and was able to do it. Here are the screenshots of the problems on my \u201cTinyBlackboard\u201d. I hope everyone got a clear understanding of the first part of Ch.14.<\/p>\n\n\n\n<p>Lesson Review:<\/p>\n\n\n\n<ul><li>an inverse: b*b^(-1) is congruent to 1 (mod m)<\/li><li>only if gcd (m,r)=1, otherwise r has no reverse modulo m.<\/li><\/ul>\n\n\n\n<p>Extra Resource:<\/p>\n\n\n\n<ul><li><a href=\"https:\/\/mathworld.wolfram.com\/LinearCongruenceEquation.html\">https:\/\/mathworld.wolfram.com\/LinearCongruenceEquation.html<\/a><\/li><li><a href=\"https:\/\/www.youtube.com\/watch?v=4-HSjLXrfPs\">https:\/\/www.youtube.com\/watch?v=4-HSjLXrfPs<\/a><\/li><li><a href=\"https:\/\/math.libretexts.org\/Bookshelves\/Combinatorics_and_Discrete_Mathematics\/Book%3A_Elementary_Number_Theory_(Raji)\/03%3A_Congruences\/3.03%3A_Linear_Congruences\">https:\/\/math.libretexts.org\/Bookshelves\/Combinatorics_and_Discrete_Mathematics\/Book%3A_Elementary_Number_Theory_(Raji)\/03%3A_Congruences\/3.03%3A_Linear_Congruences<\/a><\/li><\/ul>\n\n\n\n<p>Homework:<\/p>\n\n\n\n<ul><li>P260 Problem 14.1-14.5<\/li><li>P264, Ex 14.2.1-14.2.3<\/li><\/ul>\n\n\n\n<p>Plan for the following weeks:<\/p>\n\n\n\n<ul><li>6\/7: Ch.14 (II)<\/li><li>6\/14: Ch.15<\/li><li>6\/21: Final Exam<\/li><\/ul>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" width=\"768\" height=\"1024\" src=\"http:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0371-768x1024.jpg\" alt=\"\" class=\"wp-image-495\" srcset=\"https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0371-768x1024.jpg 768w, https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0371-225x300.jpg 225w, https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0371.jpg 1536w\" sizes=\"(max-width: 768px) 100vw, 768px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" width=\"768\" height=\"1024\" src=\"http:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0372-768x1024.jpg\" alt=\"\" class=\"wp-image-496\" srcset=\"https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0372-768x1024.jpg 768w, https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0372-225x300.jpg 225w, https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0372.jpg 1536w\" sizes=\"(max-width: 768px) 100vw, 768px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" width=\"768\" height=\"1024\" src=\"http:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0374-768x1024.jpg\" alt=\"\" class=\"wp-image-497\" srcset=\"https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0374-768x1024.jpg 768w, https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0374-225x300.jpg 225w, https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0374.jpg 1536w\" sizes=\"(max-width: 768px) 100vw, 768px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" width=\"768\" height=\"1024\" src=\"http:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0377-768x1024.jpg\" alt=\"\" class=\"wp-image-498\" srcset=\"https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0377-768x1024.jpg 768w, https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0377-225x300.jpg 225w, https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0377.jpg 1536w\" sizes=\"(max-width: 768px) 100vw, 768px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" width=\"768\" height=\"1024\" src=\"http:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0379-768x1024.jpg\" alt=\"\" class=\"wp-image-499\" srcset=\"https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0379-768x1024.jpg 768w, https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0379-225x300.jpg 225w, https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0379.jpg 1536w\" sizes=\"(max-width: 768px) 100vw, 768px\" \/><\/figure>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Sorry about the technical issue that I could not connect my iPad to Zoom in class today. Later on, I downloaded the newest version of Zoom and was able to do it. Here are the screenshots of the problems on my \u201cTinyBlackboard\u201d. I hope everyone got a clear understanding of the first part of Ch.14. [&hellip;]<\/p>\n","protected":false},"author":157,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0},"categories":[4],"tags":[],"_links":{"self":[{"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/posts\/494"}],"collection":[{"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/users\/157"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/comments?post=494"}],"version-history":[{"count":1,"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/posts\/494\/revisions"}],"predecessor-version":[{"id":500,"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/posts\/494\/revisions\/500"}],"wp:attachment":[{"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/media?parent=494"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/categories?post=494"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/tags?post=494"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}