{"id":302,"date":"2020-03-02T02:30:59","date_gmt":"2020-03-02T02:30:59","guid":{"rendered":"http:\/\/blog.newtonchineseschool.org\/lilijia\/?p=302"},"modified":"2020-03-02T02:40:38","modified_gmt":"2020-03-02T02:40:38","slug":"aops_number_theory-2020-spring-chapter-3-multiplications-and-divisions","status":"publish","type":"post","link":"https:\/\/blog.newtonchineseschool.org\/lilijia\/2020\/03\/02\/aops_number_theory-2020-spring-chapter-3-multiplications-and-divisions\/","title":{"rendered":"AoPS_Number_Theory 2020 Spring Chapter 3:  Multiplications and Divisions"},"content":{"rendered":"\n<p><strong>Lesson Review:<\/strong><\/p>\n\n\n\n<ul><li>Common divisor<\/li><li>GCD (Greatest  Common Divisor) or GCF (Greatest Common Factor) <\/li><li>Relatively prime or coprime<\/li><li>Common multiple<\/li><li>LCM (Least Common Multiple)<\/li><li>gcd(m,n)<\/li><li>lcm[m,n]<\/li><li>The Division Theorem:      a = bq + r (0\u2264r&lt;b)   a:dividend,      b:divisor, q: quotient, r: remainder<\/li><li>Euclidean algorithm:      gcd(m,n) = gcd (m-n,n)<\/li><li>The extended Euclidean algorithm: gcd(m,n) = gcd (m-n,n) = gcd (m-kn,n) = gcd (r,n)<\/li><\/ul>\n\n\n\n<p><strong>Homework: <\/strong><\/p>\n\n\n\n<ul><li>Page 40: Ex 3.2.5<\/li><li>Page 43: Ex 3.3.2<\/li><li>Page 45: Ex 3.4.1 (d) (g)<\/li><li>Page 50:\nEx 3.5.3<\/li><li>Page 53:\n3.6.1, 3.6.6<\/li><li>Page 59:\n3.7.1 (b)<\/li><li>Page 61:\n3.24 (d), 3.32, 3.33, 3.34<\/li><\/ul>\n\n\n\n<p><strong>Other Resources:<\/strong><\/p>\n\n\n\n<ul><li><a href=\"https:\/\/www.khanacademy.org\/computing\/computer-science\/cryptography\/modarithmetic\/a\/the-euclidean-algorithm\">https:\/\/www.khanacademy.org\/computing\/computer-science\/cryptography\/modarithmetic\/a\/the-euclidean-algorithm<\/a><\/li><li><a href=\"https:\/\/www.khanacademy.org\/math\/pre-algebra\/pre-algebra-factors-multiples\/pre-algebra-greatest-common-divisor\/v\/greatest-common-divisor\">https:\/\/www.khanacademy.org\/math\/pre-algebra\/pre-algebra-factors-multiples\/pre-algebra-greatest-common-divisor\/v\/greatest-common-divisor<\/a><\/li><\/ul>\n\n\n\n<p>Take care, and wish everyone to stay safe and healthy!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Lesson Review: Common divisor GCD (Greatest Common Divisor) or GCF (Greatest Common Factor) Relatively prime or coprime Common multiple LCM (Least Common Multiple) gcd(m,n) lcm[m,n] The Division Theorem: a = bq + r (0\u2264r&lt;b) a:dividend, b:divisor, q: quotient, r: remainder Euclidean algorithm: gcd(m,n) = gcd (m-n,n) The extended Euclidean algorithm: gcd(m,n) = gcd (m-n,n) = [&hellip;]<\/p>\n","protected":false},"author":157,"featured_media":0,"comment_status":"closed","ping_status":"open","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\/302"}],"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=302"}],"version-history":[{"count":2,"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/posts\/302\/revisions"}],"predecessor-version":[{"id":304,"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/posts\/302\/revisions\/304"}],"wp:attachment":[{"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/media?parent=302"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/categories?post=302"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/tags?post=302"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}