{"id":6796,"date":"2022-10-12T22:36:28","date_gmt":"2022-10-12T22:36:28","guid":{"rendered":"https:\/\/presswiki.allmath.gr\/wpwiki18\/?p=6796"},"modified":"2022-10-12T22:42:56","modified_gmt":"2022-10-12T22:42:56","slug":"%ce%ad%ce%bd%ce%b1-%cf%83%cf%8d%cf%83%cf%84%ce%b7%ce%bc%ce%b1-%cf%86%cf%85%cf%83%ce%b9%ce%ba%cf%8e%ce%bd-%ce%b1%cf%81%ce%b9%ce%b8%ce%bc%cf%8e%ce%bd","status":"publish","type":"post","link":"https:\/\/presswiki.allmath.gr\/wpwiki18\/2022\/10\/12\/22\/36\/28\/6796\/","title":{"rendered":"\u0388\u03bd\u03b1 \u03c3\u03cd\u03c3\u03c4\u03b7\u03bc\u03b1 \u03c6\u03c5\u03c3\u03b9\u03ba\u03ce\u03bd \u03b1\u03c1\u03b9\u03b8\u03bc\u03ce\u03bd."},"content":{"rendered":"\n<figure class=\"wp-block-image size-full\"><img width=\"783\" height=\"134\" src=\"https:\/\/presswiki.allmath.gr\/wpwiki18\/wp-content\/uploads\/2022\/10\/\u03b5\u03b9\u03ba\u03cc\u03bd\u03b1-22.png\" alt=\"\" class=\"wp-image-6797\" srcset=\"https:\/\/presswiki.allmath.gr\/wpwiki18\/wp-content\/uploads\/2022\/10\/\u03b5\u03b9\u03ba\u03cc\u03bd\u03b1-22.png 783w, https:\/\/presswiki.allmath.gr\/wpwiki18\/wp-content\/uploads\/2022\/10\/\u03b5\u03b9\u03ba\u03cc\u03bd\u03b1-22-300x51.png 300w, https:\/\/presswiki.allmath.gr\/wpwiki18\/wp-content\/uploads\/2022\/10\/\u03b5\u03b9\u03ba\u03cc\u03bd\u03b1-22-768x131.png 768w\" sizes=\"(max-width: 709px) 85vw, (max-width: 909px) 67vw, (max-width: 984px) 61vw, (max-width: 1362px) 45vw, 600px\" \/><\/figure>\n\n\n\n<!--nextpage-->\n\n\n\n<h2>\u039b\u03cd\u03c3\u03b7<\/h2>\n\n\n\n<p>\u03a0\u03b1\u03c1\u03b1\u03c4\u03b7\u03c1\u03bf\u03cd\u03bc\u03b5 \u03cc\u03c4\u03b9 \u03bc\u03af\u03b1 \u03bb\u03cd\u03c3\u03b7 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b7 \\( (x,y,z) = (1,1,1) \\). \u0398\u03b1 \u03b4\u03b5\u03af\u03be\u03bf\u03c5\u03bc\u03b5 \u03cc\u03c4\u03b9 \u03b5\u03af\u03bd\u03b1\u03b9 \u03ba\u03b1\u03b9 \u03b7 \u03bc\u03bf\u03bd\u03b1\u03b4\u03b9\u03ba\u03ae \u03bb\u03cd\u03c3\u03b7 \u03c4\u03bf\u03c5 \u03c3\u03c5\u03c3\u03c4\u03ae\u03bc\u03b1\u03c4\u03bf\u03c2.<\/p>\n\n\n\n<p>\u0391\u03c6\u03b1\u03b9\u03c1\u03ce\u03bd\u03c4\u03b1\u03c2 \u03c4\u03b9\u03c2 (1)-(2) \u03ad\u03c7\u03bf\u03c5\u03bc\u03b5: <\/p>\n\n\n\n<p>\\( x+y^2 + z^3 &#8211; y &#8211; z^2 &#8211; x^3 = 0 \\Leftrightarrow  x(1-x^2 ) + y(y-1) + z^2 (z-1) =0 [4]\\)<\/p>\n\n\n\n<p>\u039f\u03bc\u03bf\u03af\u03c9\u03c2 \u03bb\u03b1\u03bc\u03b2\u03ac\u03bd\u03bf\u03c5\u03bc\u03b5 \u03b1\u03c0\u03cc (2)-(3):<\/p>\n\n\n\n<p>\\( y(1-y^2 ) + z (z-1) + x^2 (x-1) = 0 [5] \\)<\/p>\n\n\n\n<p>\u039a\u03b1\u03b9 \u03c4\u03ce\u03c1\u03b1 \u03bc\u03b5 \u03c4\u03b7 \u03b4\u03b9\u03b1\u03c6\u03bf\u03c1\u03ac (4) &#8211; z (5) \u03c0\u03b1\u03af\u03c1\u03bd\u03bf\u03c5\u03bc\u03b5: <\/p>\n\n\n\n<p>\\( x(x-1)(1+x+xz) = y(y-1)(1+z+yz) [6]\\)<\/p>\n\n\n\n<p>\u03ba\u03b1\u03b9 \u03bf\u03bc\u03bf\u03af\u03c9\u03c2: <\/p>\n\n\n\n<p>\\( y(y-1)(1+y+yx) = z(z-1)(1+x+zx) [7] \\)<\/p>\n\n\n\n<p>\u0395\u03c6\u03cc\u03c3\u03bf\u03bd \u03bf\u03b9 \\(x,y,z\\) \u03b5\u03af\u03bd\u03b1\u03b9 \u03b8\u03b5\u03c4\u03b9\u03ba\u03bf\u03af, \u03b8\u03b1 \u03b9\u03c3\u03c7\u03cd\u03b5\u03b9 \u03cc\u03c4\u03b9 \u03bf\u03b9 \u03c0\u03b1\u03c1\u03ac\u03b3\u03bf\u03bd\u03c4\u03b5\u03c2 \\( (1+x+xz) , (1+z+zy) , (1+y+yx)\\) \u03b8\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b5\u03c0\u03af\u03c3\u03b7\u03c2 \u03b8\u03b5\u03c4\u03b9\u03ba\u03bf\u03af.<\/p>\n\n\n\n<p>\u039f\u03c0\u03cc\u03c4\u03b5, \u03bf\u03b9 \\( (x-1) , (y-1) , (z-1) \\) \u03b5\u03af\u03bd\u03b1\u03b9 \u03cc\u03bb\u03bf\u03b9 \u03b1\u03c1\u03bd\u03b7\u03c4\u03b9\u03ba\u03bf\u03af, \u03ae \u03b8\u03b5\u03c4\u03b9\u03ba\u03bf\u03af \u03ae \u03bc\u03b7\u03b4\u03ad\u03bd \u03ba\u03b1\u03b9 \u03bc\u03c0\u03bf\u03c1\u03b5\u03af \u03bd\u03b1 \u03b9\u03c3\u03c7\u03cd\u03b5\u03b9 \u03bc\u03cc\u03bd\u03bf \u03c4\u03bf \u03b4\u03b5\u03cd\u03c4\u03b5\u03c1\u03bf, \u03ac\u03c1\u03b1 \u03b7 \u03bb\u03cd\u03c3\u03b7 \u03c0\u03bf\u03c5 \u03b2\u03c1\u03ad\u03b8\u03b7\u03ba\u03b5 \u03b5\u03af\u03bd\u03b1\u03b9 \u03bc\u03bf\u03bd\u03b1\u03b4\u03b9\u03ba\u03ae !<\/p>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[17,54,62],"tags":[784,156],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/presswiki.allmath.gr\/wpwiki18\/wp-json\/wp\/v2\/posts\/6796"}],"collection":[{"href":"https:\/\/presswiki.allmath.gr\/wpwiki18\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/presswiki.allmath.gr\/wpwiki18\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/presswiki.allmath.gr\/wpwiki18\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/presswiki.allmath.gr\/wpwiki18\/wp-json\/wp\/v2\/comments?post=6796"}],"version-history":[{"count":3,"href":"https:\/\/presswiki.allmath.gr\/wpwiki18\/wp-json\/wp\/v2\/posts\/6796\/revisions"}],"predecessor-version":[{"id":6802,"href":"https:\/\/presswiki.allmath.gr\/wpwiki18\/wp-json\/wp\/v2\/posts\/6796\/revisions\/6802"}],"wp:attachment":[{"href":"https:\/\/presswiki.allmath.gr\/wpwiki18\/wp-json\/wp\/v2\/media?parent=6796"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/presswiki.allmath.gr\/wpwiki18\/wp-json\/wp\/v2\/categories?post=6796"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/presswiki.allmath.gr\/wpwiki18\/wp-json\/wp\/v2\/tags?post=6796"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}