{"id":106,"date":"2020-07-01T18:27:45","date_gmt":"2020-07-01T18:27:45","guid":{"rendered":"https:\/\/integrations.pressbooks.network\/mathtest\/chapter\/riemanns-life-and-times\/"},"modified":"2023-06-14T16:21:40","modified_gmt":"2023-06-14T16:21:40","slug":"riemanns-life-and-times","status":"publish","type":"chapter","link":"https:\/\/integrations.pressbooks.network\/mathtest\/chapter\/riemanns-life-and-times\/","title":{"raw":"Wrapped in [latex] shortcodes","rendered":"Wrapped in [latex] shortcodes"},"content":{"raw":"<p style=\"text-align: justify;\">In the 17th century, Pierre de Fermat had discovered many intriguing results about them, such as the fact that every prime number of the form [latex]4n + 1[\/latex] for some integer n is a sum of two squares. For example, [latex]5 = 4 \\times 1 + 1 = 2^2 + 1^2[\/latex]\u00a0 and [latex]13 = 4 \\times 3 + 1 = 3^2 + 2^2[\/latex]. He also had a proof that there are no integers [latex]x, y, z[\/latex]\u00a0greater than 1, such that<\/p>\r\n<p style=\"text-align: center;\">[latex]x^4 + y^4 = z^4.[\/latex]<\/p>\r\n<p class=\"no-indent\" style=\"text-align: justify;\">He had even incautiously committed himself to the statement that there are no integers <em>x, y, z<\/em> greater than 1, such that<\/p>\r\n<p style=\"text-align: center;\">[latex]x^n + y^n = z^n.[\/latex]<\/p>\r\n<p style=\"text-align: justify;\">for any integer [latex]n[\/latex]\u00a0other than 1 or 2.<\/p>","rendered":"<p style=\"text-align: justify;\">In the 17th century, Pierre de Fermat had discovered many intriguing results about them, such as the fact that every prime number of the form [latex]4n + 1[\/latex] for some integer n is a sum of two squares. For example, [latex]5 = 4 \\times 1 + 1 = 2^2 + 1^2[\/latex]\u00a0 and [latex]13 = 4 \\times 3 + 1 = 3^2 + 2^2[\/latex]. He also had a proof that there are no integers [latex]x, y, z[\/latex]\u00a0greater than 1, such that<\/p>\n<p style=\"text-align: center;\">[latex]x^4 + y^4 = z^4.[\/latex]<\/p>\n<p class=\"no-indent\" style=\"text-align: justify;\">He had even incautiously committed himself to the statement that there are no integers <em>x, y, z<\/em> greater than 1, such that<\/p>\n<p style=\"text-align: center;\">[latex]x^n + y^n = z^n.[\/latex]<\/p>\n<p style=\"text-align: justify;\">for any integer [latex]n[\/latex]\u00a0other than 1 or 2.<\/p>\n","protected":false},"author":14,"menu_order":2,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":["morty","mark"],"pb_section_license":""},"chapter-type":[],"contributor":[67,69],"license":[],"class_list":["post-106","chapter","type-chapter","status-publish","hentry","contributor-mark","contributor-morty"],"part":3,"_links":{"self":[{"href":"https:\/\/integrations.pressbooks.network\/mathtest\/wp-json\/pressbooks\/v2\/chapters\/106","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/integrations.pressbooks.network\/mathtest\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/integrations.pressbooks.network\/mathtest\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/integrations.pressbooks.network\/mathtest\/wp-json\/wp\/v2\/users\/14"}],"version-history":[{"count":2,"href":"https:\/\/integrations.pressbooks.network\/mathtest\/wp-json\/pressbooks\/v2\/chapters\/106\/revisions"}],"predecessor-version":[{"id":171,"href":"https:\/\/integrations.pressbooks.network\/mathtest\/wp-json\/pressbooks\/v2\/chapters\/106\/revisions\/171"}],"part":[{"href":"https:\/\/integrations.pressbooks.network\/mathtest\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/integrations.pressbooks.network\/mathtest\/wp-json\/pressbooks\/v2\/chapters\/106\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/integrations.pressbooks.network\/mathtest\/wp-json\/wp\/v2\/media?parent=106"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/integrations.pressbooks.network\/mathtest\/wp-json\/pressbooks\/v2\/chapter-type?post=106"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/integrations.pressbooks.network\/mathtest\/wp-json\/wp\/v2\/contributor?post=106"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/integrations.pressbooks.network\/mathtest\/wp-json\/wp\/v2\/license?post=106"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}