{"id":21183,"date":"2020-11-01T04:04:05","date_gmt":"2020-11-01T03:04:05","guid":{"rendered":"https:\/\/xmau.com\/wp\/notiziole\/?p=21183"},"modified":"2020-10-31T23:00:08","modified_gmt":"2020-10-31T22:00:08","slug":"quizzino-della-domenica-polinomi","status":"publish","type":"post","link":"https:\/\/xmau.com\/wp\/notiziole\/2020\/11\/01\/quizzino-della-domenica-polinomi\/","title":{"rendered":"Quizzino della domenica: polinomi"},"content":{"rendered":"<div class='__iawmlf-post-loop-links' style='display:none;' data-iawmlf-post-links='[{&quot;id&quot;:3524,&quot;href&quot;:&quot;http:\\\/\\\/xmau.com\\\/quizzini\\\/p481.html&quot;,&quot;archived_href&quot;:&quot;http:\\\/\\\/web-wp.archive.org\\\/web\\\/20210125102130\\\/https:\\\/\\\/xmau.com\\\/quizzini\\\/p481.html&quot;,&quot;redirect_href&quot;:&quot;&quot;,&quot;checks&quot;:[{&quot;date&quot;:&quot;2026-02-13 12:13:37&quot;,&quot;http_code&quot;:206},{&quot;date&quot;:&quot;2026-02-16 21:17:42&quot;,&quot;http_code&quot;:206},{&quot;date&quot;:&quot;2026-02-20 03:22:06&quot;,&quot;http_code&quot;:206},{&quot;date&quot;:&quot;2026-02-23 04:10:23&quot;,&quot;http_code&quot;:206},{&quot;date&quot;:&quot;2026-02-27 00:37:09&quot;,&quot;http_code&quot;:206},{&quot;date&quot;:&quot;2026-03-03 18:24:31&quot;,&quot;http_code&quot;:206},{&quot;date&quot;:&quot;2026-03-06 20:23:55&quot;,&quot;http_code&quot;:206},{&quot;date&quot;:&quot;2026-03-11 11:37:20&quot;,&quot;http_code&quot;:206},{&quot;date&quot;:&quot;2026-03-17 13:06:21&quot;,&quot;http_code&quot;:206},{&quot;date&quot;:&quot;2026-03-21 23:18:20&quot;,&quot;http_code&quot;:206},{&quot;date&quot;:&quot;2026-03-25 14:00:10&quot;,&quot;http_code&quot;:206},{&quot;date&quot;:&quot;2026-03-30 18:30:00&quot;,&quot;http_code&quot;:206},{&quot;date&quot;:&quot;2026-04-03 17:38:25&quot;,&quot;http_code&quot;:206},{&quot;date&quot;:&quot;2026-04-08 19:52:43&quot;,&quot;http_code&quot;:206},{&quot;date&quot;:&quot;2026-04-12 22:11:28&quot;,&quot;http_code&quot;:206},{&quot;date&quot;:&quot;2026-04-18 14:38:20&quot;,&quot;http_code&quot;:206}],&quot;broken&quot;:false,&quot;last_checked&quot;:{&quot;date&quot;:&quot;2026-04-18 14:38:20&quot;,&quot;http_code&quot;:206},&quot;process&quot;:&quot;done&quot;},{&quot;id&quot;:3525,&quot;href&quot;:&quot;https:\\\/\\\/twitter.com\\\/DavidKButlerUoA\\\/status\\\/1318294991500832768&quot;,&quot;archived_href&quot;:&quot;http:\\\/\\\/web-wp.archive.org\\\/web\\\/20201019205702\\\/https:\\\/\\\/twitter.com\\\/DavidKButlerUoA\\\/status\\\/1318294991500832768&quot;,&quot;redirect_href&quot;:&quot;&quot;,&quot;checks&quot;:[{&quot;date&quot;:&quot;2026-02-13 12:13:40&quot;,&quot;http_code&quot;:200},{&quot;date&quot;:&quot;2026-02-16 21:17:43&quot;,&quot;http_code&quot;:200},{&quot;date&quot;:&quot;2026-02-20 03:22:06&quot;,&quot;http_code&quot;:200},{&quot;date&quot;:&quot;2026-02-23 04:10:22&quot;,&quot;http_code&quot;:200},{&quot;date&quot;:&quot;2026-02-27 00:37:07&quot;,&quot;http_code&quot;:200},{&quot;date&quot;:&quot;2026-03-03 18:24:31&quot;,&quot;http_code&quot;:200},{&quot;date&quot;:&quot;2026-03-06 20:23:54&quot;,&quot;http_code&quot;:200},{&quot;date&quot;:&quot;2026-03-11 11:37:22&quot;,&quot;http_code&quot;:200},{&quot;date&quot;:&quot;2026-03-17 13:06:20&quot;,&quot;http_code&quot;:200},{&quot;date&quot;:&quot;2026-03-21 23:18:19&quot;,&quot;http_code&quot;:200},{&quot;date&quot;:&quot;2026-03-25 14:00:08&quot;,&quot;http_code&quot;:200},{&quot;date&quot;:&quot;2026-03-30 18:29:59&quot;,&quot;http_code&quot;:200},{&quot;date&quot;:&quot;2026-04-03 17:38:30&quot;,&quot;http_code&quot;:503},{&quot;date&quot;:&quot;2026-04-08 19:52:42&quot;,&quot;http_code&quot;:404},{&quot;date&quot;:&quot;2026-04-12 22:11:28&quot;,&quot;http_code&quot;:200},{&quot;date&quot;:&quot;2026-04-18 14:38:21&quot;,&quot;http_code&quot;:200}],&quot;broken&quot;:false,&quot;last_checked&quot;:{&quot;date&quot;:&quot;2026-04-18 14:38:21&quot;,&quot;http_code&quot;:200},&quot;process&quot;:&quot;done&quot;}]'><\/div>\n<p>\u00c8 ovvio che se prendiamo un polinomio in una variabile <i>x<\/i> a coefficienti interi, come 3<i>x<\/i>&sup3;+14<i>x<\/i>&sup2;+15<i>x<\/i>+10, e assegniamo a <i>x<\/i> un valore intero otteniamo un risultato intero. Ma \u00e8 vero anche il viceversa? In altri termini: se abbiamo un polinomio in <i>x<\/i> che ha un valore intero per un qualunque valore intero assegnato a <i>x<\/i>, possiamo dedurre che quel polinomio \u00e8 a coefficienti interi?<\/p>\n<p><!-- Il prodotto di due interi consecutivi \u00e8 pari. --><br \/>\n<img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/xmau.com\/wp\/notiziole\/wp-content\/uploads\/sites\/6\/2020\/10\/q481a.png?resize=543%2C86&#038;ssl=1\" alt=\"polinomio\" width=\"543\" height=\"86\" class=\"aligncenter size-full wp-image-21185\" srcset=\"https:\/\/i0.wp.com\/xmau.com\/wp\/notiziole\/wp-content\/uploads\/sites\/6\/2020\/10\/q481a.png?w=543&amp;ssl=1 543w, https:\/\/i0.wp.com\/xmau.com\/wp\/notiziole\/wp-content\/uploads\/sites\/6\/2020\/10\/q481a.png?resize=300%2C48&amp;ssl=1 300w, https:\/\/i0.wp.com\/xmau.com\/wp\/notiziole\/wp-content\/uploads\/sites\/6\/2020\/10\/q481a.png?resize=500%2C79&amp;ssl=1 500w\" sizes=\"auto, (max-width: 543px) 100vw, 543px\" \/><\/p>\n<p><small>(trovate un aiutino sul mio sito, alla pagina <a href=\"http:\/\/xmau.com\/quizzini\/p481.html\">http:\/\/xmau.com\/quizzini\/p481.html<\/a>; la risposta verr\u00e0 postata l\u00ec il prossimo mercoled\u00ec. Problema di <a href=\"https:\/\/twitter.com\/DavidKButlerUoA\/status\/1318294991500832768\">David Butler<\/a>.)<\/small><\/p>\n<p><!-- La risposta \u00e8 no. Un esempio \u00e8 il polinomio (1\/2)x&sup2;+(1\/2)x. Se lo scriviamo come x(x+1)\/2, vediamo subito che per qualunque intero x il numeratore \u00e8 sempre pari, perch\u00e9 prodotto di due interi positivi, e quindi il suo valore complessivo \u00e8 sempre un intero. --><\/p>\n<p><!-- Se vi consola, io non c'ero arrivato. --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u00c8 ovvio che se prendiamo un polinomio in una variabile x a coefficienti interi, come 3x&sup3;+14x&sup2;+15x+10, e assegniamo a x un valore intero otteniamo un risultato intero. Ma \u00e8 vero anche il viceversa? In altri termini: se abbiamo un polinomio in x che ha un valore intero per un qualunque valore intero assegnato a x, [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_lmt_disableupdate":"","_lmt_disable":"","jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"activitypub_content_warning":"","activitypub_content_visibility":"","activitypub_max_image_attachments":3,"activitypub_interaction_policy_quote":"anyone","activitypub_status":"","footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[74,937],"tags":[],"class_list":["post-21183","post","type-post","status-publish","format-standard","hentry","category-giochi","category-giochi-2020"],"modified_by":".mau.","jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p6hcSh-5vF","jetpack-related-posts":[{"id":7771,"url":"https:\/\/xmau.com\/wp\/notiziole\/2010\/03\/17\/un_problema_sui\/","url_meta":{"origin":21183,"position":0},"title":"Un problema sui polinomi","author":".mau.","date":"2010-03-17","format":false,"excerpt":"Non sembra, ma dare dei vincoli sui coefficienti di un polinomio restringe davvero le possibilit\u00e0!","rel":"","context":"In &quot;matematica_light&quot;","block_context":{"text":"matematica_light","link":"https:\/\/xmau.com\/wp\/notiziole\/category\/matematica_light\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":36180,"url":"https:\/\/xmau.com\/wp\/notiziole\/2026\/03\/04\/i-dadi-di-sicherman\/","url_meta":{"origin":21183,"position":1},"title":"I dadi di Sicherman","author":".mau.","date":"2026-03-04","format":false,"excerpt":"Due dadi che hanno la stessa distribuzione di risultati di quelli standard, ma i cui numeri sono diversi","rel":"","context":"In &quot;mate-light 2026&quot;","block_context":{"text":"mate-light 2026","link":"https:\/\/xmau.com\/wp\/notiziole\/category\/matematica_light\/matelight-2026\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":27711,"url":"https:\/\/xmau.com\/wp\/notiziole\/2023\/11\/15\/il-paradosso-di-sierpinski-mazurkiewicz\/","url_meta":{"origin":21183,"position":2},"title":"Il paradosso di Sierpinski-Mazurkiewicz","author":".mau.","date":"2023-11-15","format":false,"excerpt":"i numeri reali sono davvero tanti, e cos\u00ec arrivano i paradossi.","rel":"","context":"In &quot;matematica_light&quot;","block_context":{"text":"matematica_light","link":"https:\/\/xmau.com\/wp\/notiziole\/category\/matematica_light\/"},"img":{"alt_text":"ma anche senza assioma della scelta...","src":"https:\/\/i0.wp.com\/xmau.com\/wp\/notiziole\/wp-content\/uploads\/sites\/6\/2023\/11\/banach-tarski.jpg?resize=350%2C200&ssl=1","width":350,"height":200},"classes":[]},{"id":31295,"url":"https:\/\/xmau.com\/wp\/notiziole\/2025\/02\/05\/numeri-duali-e-numeri-conplessi-iperbolici\/","url_meta":{"origin":21183,"position":3},"title":"Numeri duali e numeri complessi iperbolici","author":".mau.","date":"2025-02-05","format":false,"excerpt":"Per fare i numeri immaginari aggiungiamo un \"valore esterno\" i per cui i\u00b2 = \u22121. Se aggiungessimo un valore diverso che succede?","rel":"","context":"In &quot;mate-light-2025&quot;","block_context":{"text":"mate-light-2025","link":"https:\/\/xmau.com\/wp\/notiziole\/category\/matematica_light\/matelight-2025\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":29146,"url":"https:\/\/xmau.com\/wp\/notiziole\/2024\/06\/19\/quando-la-fattorizzazione-non-e-unica\/","url_meta":{"origin":21183,"position":4},"title":"Quando la fattorizzazione non \u00e8 unica","author":".mau.","date":"2024-06-19","format":false,"excerpt":"quasi sempre, purtroppo","rel":"","context":"In &quot;mate-light-2024&quot;","block_context":{"text":"mate-light-2024","link":"https:\/\/xmau.com\/wp\/notiziole\/category\/matematica_light\/matelight-2024\/"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/xmau.com\/wp\/notiziole\/wp-content\/uploads\/sites\/6\/2024\/06\/163.png?resize=350%2C200&ssl=1","width":350,"height":200},"classes":[]},{"id":31816,"url":"https:\/\/xmau.com\/wp\/notiziole\/2025\/03\/19\/il-teorema-di-lin-mcmullin\/","url_meta":{"origin":21183,"position":5},"title":"Il teorema di Lin McMullin","author":".mau.","date":"2025-03-19","format":false,"excerpt":"Il rapporto aureo spunta nei posti pi\u00f9 impensati.","rel":"","context":"In &quot;mate-light-2025&quot;","block_context":{"text":"mate-light-2025","link":"https:\/\/xmau.com\/wp\/notiziole\/category\/matematica_light\/matelight-2025\/"},"img":{"alt_text":"Rappresentazione grafica del teorema di McMullin","src":"https:\/\/i0.wp.com\/xmau.com\/wp\/notiziole\/wp-content\/uploads\/sites\/6\/2025\/03\/McMullin.jpg?resize=350%2C200&ssl=1","width":350,"height":200},"classes":[]}],"jetpack_likes_enabled":true,"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/xmau.com\/wp\/notiziole\/wp-json\/wp\/v2\/posts\/21183","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/xmau.com\/wp\/notiziole\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/xmau.com\/wp\/notiziole\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/xmau.com\/wp\/notiziole\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/xmau.com\/wp\/notiziole\/wp-json\/wp\/v2\/comments?post=21183"}],"version-history":[{"count":4,"href":"https:\/\/xmau.com\/wp\/notiziole\/wp-json\/wp\/v2\/posts\/21183\/revisions"}],"predecessor-version":[{"id":21230,"href":"https:\/\/xmau.com\/wp\/notiziole\/wp-json\/wp\/v2\/posts\/21183\/revisions\/21230"}],"wp:attachment":[{"href":"https:\/\/xmau.com\/wp\/notiziole\/wp-json\/wp\/v2\/media?parent=21183"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/xmau.com\/wp\/notiziole\/wp-json\/wp\/v2\/categories?post=21183"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/xmau.com\/wp\/notiziole\/wp-json\/wp\/v2\/tags?post=21183"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}