{"id":44920,"date":"2025-08-07T09:19:35","date_gmt":"2025-08-07T09:19:35","guid":{"rendered":"https:\/\/fram.is\/?p=44920"},"modified":"2025-08-07T09:20:12","modified_gmt":"2025-08-07T09:20:12","slug":"af-fullkomnum-og-ofullkomnum-tolum","status":"publish","type":"post","link":"http:\/\/fram.is\/is\/2025\/08\/07\/af-fullkomnum-og-ofullkomnum-tolum\/","title":{"rendered":"Af fullkomnum og \u00f3fullkomnum t\u00f6lum"},"content":{"rendered":"
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N\u00e1tt\u00faruleg tala er s\u00f6g\u00f0 fullkomin, ef h\u00fan er j\u00f6fn summu allra \u00feeirra talna sem eru minni en h\u00fan sj\u00e1lf og ganga upp \u00ed henni. \u00deannig er 6 fullkomin tala, \u00fev\u00ed 6 = 1 + 2 + 3, og einnig er 28 fullkomin, \u00fev\u00ed 28 = 1 + 2 + 4 + 7 + 14. \u00der\u00e1tt fyrir a\u00f0 fullkomnar t\u00f6lur hafi veri\u00f0 \u00feekktar \u00ed langan t\u00edma \u00e1 enn eftir a\u00f0 svara fj\u00f6lm\u00f6rgum spurningum um \u00fe\u00e6r, meira p\u00fa\u00f0ur hefur hins vegar fari\u00f0 \u00ed ranns\u00f3knir \u00e1 frumt\u00f6lum, sem er gali\u00f0. Til d\u00e6mis er alls ekki vita\u00f0 hvort til s\u00e9 fullkomin oddatala og eru a\u00f0eins 44 fullkomnar t\u00f6lur \u00feekktar \u00ed dag.<\/p>

\u00deegar st\u00f6\u00f0utaflan var sko\u00f0u\u00f0 fyrir leik kveldsins kom \u00ed lj\u00f3s a\u00f0 li\u00f0in v\u00e6ru a\u00f0 vinna me\u00f0 s\u00f6mu hugmyndafr\u00e6\u00f0i og voru l\u00edkindin \u00e1\u00fereifanleg, jafnvel \u00f3\u00fe\u00e6gileg. B\u00e6\u00f0i li\u00f0 me\u00f0 24 stig eftir 16 leiki, b\u00e6\u00f0i li\u00f0 me\u00f0 7 sigra og 3 jafntefli en FRAM ra\u00f0ast oftar enda me\u00f0 4 m\u00f6rk \u00ed pl\u00fas \u00e1 me\u00f0an andst\u00e6\u00f0ingar dagsins, Gar\u00f0ahreppsmenn \u00far Stj\u00f6rnub\u00e6 voru a\u00f0eins me\u00f0 tv\u00f6 m\u00f6rk \u00ed pl\u00fas fyrir leik. H\u00e9r er r\u00e9tt a\u00f0 taka fram a\u00f0 talan 24 er ekki fullkomin tala, \u00fear sem 1, 2, 3, 4, 6, 8 og 12 ganga upp \u00ed 24, en summa \u00feeirra er 36 \u2013 \u00fei\u00f0 eru\u00f0 sem sagt b\u00fain a\u00f0 n\u00e1 \u00feessu n\u00fana.<\/p>

\u00dea\u00f0 kom \u00fev\u00ed varla \u00e1 \u00f3vart a\u00f0 flestir sparkspekingar landsins sp\u00e1\u00f0u leiknum jafntefli, janvel margir \u00e1 \u00fev\u00ed a\u00f0 \u00feetta yr\u00f0i markalaus leikur, hinn svokalla\u00f0i fullkomni knattspyrnuleikur, en galgopar \u00ed st\u00e9ttinni sp\u00e1\u00f0u a\u00f0 hvort li\u00f0 myndi skora eitt mark, jafnvel b\u00e6\u00f0i sj\u00e1lfsm\u00f6rk. Lengjustu\u00f0ullinn \u00e1 jafntefli fyrir leik var 3.69 \u2013 \u00fev\u00edl\u00edkt dau\u00f0af\u00e6ri \u00e1 a\u00f0 n\u00e1 yfirdr\u00e6ttinum ni\u00f0ur eftir sumarleyfi\u00f0. \u00a0<\/p>

L\u00edkindin endu\u00f0u ekki h\u00e9rna, heldur hafa Gar\u00f0ahreppsmenn \u00far Stj\u00f6rnub\u00e6 fengi\u00f0 til li\u00f0s vi\u00f0 sig varnarmanninn Steven Roy Caulker, en hann hefur n\u00fa a\u00f0allega fengi\u00f0 a\u00f0 verma bekkinn hinga\u00f0 til, \u00fe\u00f3 ekki alveg \u00e1 Carlosar Kaiser skala (Draugar fort\u00ed\u00f0ar \u2013 \u00fe\u00e1ttur 186). Steven hefur \u00feann \u00feunga kistil a\u00f0 bera \u00e1 her\u00f0um s\u00e9r a\u00f0 hafa eitt sinn flokkast sem leikma\u00f0ur Liverpool, og n\u00e1\u00f0 a\u00f0 taka \u00fe\u00e1tt \u00ed 3 leiknum undir stj\u00f3ranum Klopp. \u00deetta kallast n\u00fa varla frumleg n\u00e1lgun, \u00fear sem FRAM gekk fr\u00e1 s\u00ednum Liverpool tengingum fyrir nokkrum leikt\u00ed\u00f0um \u00feegar Danny Guthrie hj\u00e1lpa\u00f0i FRAMli\u00f0inu a\u00f0 komast upp \u00far Lengjudeildinni \u00e1ri\u00f0 2021. Reyndar er alneti\u00f0 \u00e1 \u00fev\u00ed a\u00f0 hann hafi spila\u00f0 17 leiki me\u00f0 okkur \u00feetta t\u00edmabil, \u00fear af f\u00f3r hann \u00ferisvar sinnum \u00fat \u00far mi\u00f0juhringnum, \u00ed \u00f6ll skiptin til a\u00f0 taka aukaspyrnu. Reyndar eru allar heimildir fr\u00e1 \u00feessum t\u00edma \u00ed sk\u00f6tul\u00edki, \u00fear sem \u00feetta var Covid sumari\u00f0 mikla og \u00e1horfendur yfirleitt banna\u00f0ir e\u00f0a me\u00f0 heila\u00feoku vegna veikinda og b\u00f3lusetninga. Og hva\u00f0 \u00e1 Danny Guthrie svo marga leiki me\u00f0 Liverpool \u00ed deildinni? J\u00fa, miki\u00f0 r\u00e9tt, au\u00f0vita\u00f0 \u00e1 hann 3 leiki, leikt\u00ed\u00f0ina 2006-7, \u00fer\u00edr er reyndar ekki fullkomin tala \u2013 en vi\u00f0 t\u00f6kum viljann fyrir verki\u00f0 hj\u00e1 \u00feeim Liverpool br\u00e6\u00f0rum.\u00a0<\/p>

\u00dea\u00f0 var \u00fev\u00ed jafnt \u00e1 \u00f6llum t\u00f6lum fyrir leik og r\u00famlega \u00fea\u00f0, sumar fullkomnar, a\u00f0rar ekki. FRAMli\u00f0i\u00f0 var a\u00f0 sleikja s\u00e1rin eftir jafntefli vi\u00f0 V\u00edkinga \u00ed s\u00ed\u00f0asta leik, \u00e1 me\u00f0an Gar\u00f0ahreppsmenn l\u00f6g\u00f0u Aftureldingu, en einungis eftir a\u00f0 f\u00e6kka\u00f0 var \u00ed li\u00f0i eldingarmanna. Vel var m\u00e6tt \u00ed heitustu st\u00faku landsins, enda var leikurinn ekki bara bar\u00e1ttan um fullkomnu t\u00f6lurnar, fullkomnu bl\u00e1u b\u00faningana, fullkomna fj\u00f3r\u00f0a s\u00e6ti\u00f0, heldur einnig hugsanleg bar\u00e1tta um fullkomi\u00f0 Evr\u00f3pus\u00e6ti, \u00fe\u00f3 svo a\u00f0 enginn hafi vilja\u00f0 vi\u00f0urkenna \u00fea\u00f0 fyrir fram. \u00c1horfendurnir sem m\u00e6ttu \u00far Gar\u00f0ahreppnum voru yfirleitt ofkl\u00e6ddir, komandi \u00far k\u00f6ldustu st\u00faku landsins, en flestir voru vel lita\u00f0ir eftir \u00e6vint\u00fdri sumarsins \u00e1 Cayman eyjum, FRAMarar sem h\u00f6f\u00f0u fari\u00f0 austur e\u00f0a nor\u00f0ur \u00ed sumar voru me\u00f0 lit, a\u00f0rir ekki.<\/p>

Allir voru m\u00e6ttir \u00e1 leikinn og \u00f6mmur \u00feeirra, Kristj\u00e1n Freyr \u00e1 R\u00e1s2, Skonrokk br\u00f3\u00f0irinn, Bj\u00f6ssi \u00deorrapabbi, Addi \u00far bankanum, Rabbi trymbill, biskupinn og b\u00edlstj\u00f3rinn og svo m\u00e6tti lengi telja. En enginn Stef\u00e1n P\u00e1lsson var \u00e1 \u00e1horfendabekkjunum, \u00fear sem hann var fastur \u00e1 fri\u00f0arr\u00e1\u00f0stefnu um kjaravopn (\u00daran \u2013 s\u00e6tistala 92, ekki fullkomin tala). Reyndar \u00e1tti r\u00e1\u00f0stefnan v\u00edst a\u00f0 kl\u00e1rast um fimmleiti\u00f0, en \u00e1 eftir fri\u00f0i kemur \u00f3fri\u00f0ur og var eflaust veri\u00f0 a\u00f0 \u00f6skursyngja Njallann e\u00f0a einhvern slagara me\u00f0 Yoko Ono er d\u00f3marinn flauta\u00f0i leikinn \u00e1, \u00ed Dal draumanna \u00ed f\u00ednasta f\u00f3tboltave\u00f0ri.<\/p>

Byrjunarli\u00f0i\u00f0 lita\u00f0ist nokku\u00f0 af banni og mei\u00f0slum. Viktor var \u00ed markinu a\u00f0 vanda, Sigurj\u00f3n var \u00ed banni og \u00fev\u00ed myndu\u00f0u Kyle, \u00deorri og Kennie \u00ferenninguna aftast. Halli og M\u00e1si \u00ed v\u00e6ngbakv\u00f6r\u00f0um, Fred, Simon og Feyr inn\u00e1 mi\u00f0junni og svo R\u00f3bert og Jakob frammi. Vuk \u00e1 bekknum eftir a\u00f0 hafa veri\u00f0 bl\u00f3\u00f0ga\u00f0ur illilega fyrir nokkru. St\u00f3ru fr\u00e9ttirnar hj\u00e1 andst\u00e6\u00f0ingunum voru a\u00f0 Liverpool ma\u00f0urinn var \u00ed byrjunarli\u00f0inu \u2013 hann er st\u00f3r og var \u00ed mj\u00f6g st\u00f3rum b\u00faningi.<\/p>

Leikurinn byrja\u00f0i a\u00f0 krafti og vorum vi\u00f0 mun sterkari. Fengum \u00e1litlegar st\u00f6\u00f0ur og f\u00e6ri eftir f\u00e6ri en ekki vildi boltinn inn. Fyrst \u00e1tti Freyr skalla eftir 2 m\u00edn\u00fatur en flj\u00f3tlega eftir \u00fea\u00f0 \u00feurfti Viktor a\u00f0 verja. Eftir 10 m\u00edn \u00e1tti Bystr\u00f6m sending \u00fat \u00ed teig \u00fear sem Fred kom og \u00e1tti \u00e1g\u00e6tt skot sem var vari\u00f0. \u00c1fram \u00e1ttum vi\u00f0 leikinn fyrir utan eitt rangst\u00f6\u00f0umark fr\u00e1 \u00feeim sem gat aldrei n\u00e1\u00f0 tali. N\u00fa f\u00f3r R\u00f3bert a\u00f0 gera sig gildandi og \u00e1tti 2 tilraunir, en ekkert gekk. \u00c1fram h\u00e9lt s\u00f3kn okkar og redda\u00f0i Liverpool ma\u00f0urinn (muni\u00f0 \u2013 bara 3 leikir) \u00feeim me\u00f0 g\u00f3\u00f0um t\u00e6kklingum og almennum tuddaskap. Enn var R\u00f3bert atkv\u00e6\u00f0amikill og \u00e1tti hann sl\u00e1arskot eftir g\u00f3\u00f0a rispu eftir 38 m\u00edn. R\u00e9tt fyrir hl\u00e9 f\u00e9kk Bystr\u00f6m a\u00f0 finna fyrir Liverpool manninum, sem f\u00e9kk r\u00e9ttilega gult kort fyrir kr\u00f6ftugt brot. Reyndar f\u00e9kk Fred stuttu s\u00ed\u00f0ar spjald fyrir n\u00e1kv\u00e6mlega engar sakir. Flauta\u00f0i d\u00f3marinn svo h\u00e1lfleikinn af og sn\u00e9rist h\u00e1lfleiksspjalli\u00f0 hj\u00e1 \u00f6llum um \u00fea\u00f0 hvers vegna \u00ed \u00f3sk\u00f6punum vi\u00f0 v\u00e6rum ekki b\u00fanir a\u00f0 ganga fr\u00e1 \u00feessum leik. Uppspil \u00feeirra \u00far Gar\u00f0ahreppi sn\u00e9rist um a\u00f0 markma\u00f0urinn setti bolta fram \u00e1 st\u00f3ra manninn frammi, sem \u00e1tti a\u00f0 n\u00e1 honum ni\u00f0ur og b\u00faa eitthva\u00f0 til \u2013 \u00fea\u00f0 gekk ekki eftir enda er \u00e1ri\u00f0 ekki 496, reyndar er \u00feetta \u00e1rtal bara nota\u00f0 til a\u00f0 koma n\u00e6stu fullkomnu t\u00f6lu a\u00f0.<\/p>

Eftir g\u00f3\u00f0an vi\u00f0gj\u00f6rning \u00e1 Bar8 me\u00f0 innliti \u00ed VIP \u2013 \u00fe\u00e1 var haldi\u00f0 \u00ed seinni h\u00e1lfleikinn me\u00f0 \u00fe\u00e1 von a\u00f0 n\u00fa k\u00e6mu m\u00f6rkin (H\u00f6skuldarvi\u00f0v\u00f6run \u2013 \u00feau komu). Seinni h\u00e1lfleikurinn byrja\u00f0i eins og s\u00e1 fyrri me\u00f0 skalla fr\u00e1 Frey. \u00c1fram vorum vi\u00f0 sterkari og \u00e1tti M\u00e1si skot eftir 7 m\u00edn\u00fatna leik en allt kom fyrir ekki. H\u00e9r hentu andst\u00e6\u00f0ingarnir \u00ed tv\u00f6falda skiptingu enda stefndi allt \u00ed \u00f3efni hj\u00e1 \u00feeim. \u00dea\u00f0 var eftir klukkut\u00edma leik a\u00f0 vi\u00f0 fengum horn sem var teki\u00f0 stutt og \u00e1tti Fred g\u00f3\u00f0a sendingu fyrir sem R\u00f3bert n\u00e1\u00f0i a\u00f0 koma boltanum \u00ed neti\u00f0, hugsanlega me\u00f0 mj\u00f6\u00f0minni e\u00f0a \u00f6\u00f0rum l\u00edkamshluta. EN hverjum er ekki sama, mark er mark og n\u00fa var pelinn tekinn til kostanna og allt var\u00f0 gott. Eftir marki\u00f0 f\u00f3r Liverpool ma\u00f0urinn a\u00f0 laumast fram \u00ed s\u00f3knina til a\u00f0 skapa ursla og t\u00f3kst \u00fea\u00f0 nokku\u00f0 vel. Vi\u00f0 l\u00f6g\u00f0umst helst til of aftarlega og skyndilega f\u00f3ru \u00feeir a\u00f0 n\u00e1 a\u00f0 manna teginn vel og skapa h\u00e6ttu. \u00c1 \u00feessu t\u00edmabili \u00e1tti Viktor g\u00f3\u00f0ar v\u00f6rslur og Kennie kom okkur oftar en einusinni til bjargar. \u00dearna var Vuk kominn inn\u00e1 fyrir Byst\u00f6m sem st\u00f3\u00f0 fyrir s\u00ednu. Gar\u00f0ahreppur h\u00e9lt \u00e1fram a\u00f0 \u00f3gna, en vi\u00f0 \u00e1ttum s\u00f3knarm\u00f6guleika inn \u00e1 milli sem ekki voru n\u00fdttir n\u00e6gilega vel. Freyr lauk svo leik og kom Tryggvi inn\u00e1. Enn var herja\u00f0 \u00e1 okkur og skoru\u00f0u \u00feeir svo \u00far horni eftir darra\u00f0ardans \u00ed teignum. Eftir marki\u00f0 jafna\u00f0ist leikurinn aftur og \u00e1ttu hvorugt li\u00f0i\u00f0 \u00e1litleg f\u00e6ri eftir \u00feetta. D\u00f3marinn kom \u00ed veg fyrir gott upphlaup okkar manna og leikurinn fjara\u00f0i \u00fat.<\/p>

\u00deetta var svona leikur \u00fear sem allir voru svekktir eftir leik, vonandi d\u00f3marinn l\u00edka me\u00f0 \u00fev\u00ed a\u00f0 taka af okkur upplagt upphlaup \u00ed restina. \u00deessi \u00farslit og \u00f6nnur \u00ed \u00feessari umfer\u00f0 gera n\u00e6sta leik fyrir vestan enn mikilv\u00e6gari ef vi\u00f0 \u00e6tlum okkur fj\u00f3r\u00f0a s\u00e6ti\u00f0.<\/p>

Skjaldsveinninn Valur Nor\u00f0ri \u00a0\u00a0\u00a0<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\t\t<\/div>","protected":false},"excerpt":{"rendered":"

N\u00e1tt\u00faruleg tala er s\u00f6g\u00f0 fullkomin, ef h\u00fan er j\u00f6fn summu allra \u00feeirra talna sem eru minni en h\u00fan sj\u00e1lf og ganga upp \u00ed henni. \u00deannig er 6 fullkomin tala, \u00fev\u00ed […]<\/p>","protected":false},"author":5,"featured_media":44921,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[9,11],"tags":[],"class_list":["post-44920","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-fotbolti","category-mflkarla"],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/fram.is\/wp-content\/uploads\/2025\/08\/Robert-.jpg","_links":{"self":[{"href":"http:\/\/fram.is\/is\/wp-json\/wp\/v2\/posts\/44920","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/fram.is\/is\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/fram.is\/is\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/fram.is\/is\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"http:\/\/fram.is\/is\/wp-json\/wp\/v2\/comments?post=44920"}],"version-history":[{"count":4,"href":"http:\/\/fram.is\/is\/wp-json\/wp\/v2\/posts\/44920\/revisions"}],"predecessor-version":[{"id":44925,"href":"http:\/\/fram.is\/is\/wp-json\/wp\/v2\/posts\/44920\/revisions\/44925"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/fram.is\/is\/wp-json\/wp\/v2\/media\/44921"}],"wp:attachment":[{"href":"http:\/\/fram.is\/is\/wp-json\/wp\/v2\/media?parent=44920"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/fram.is\/is\/wp-json\/wp\/v2\/categories?post=44920"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/fram.is\/is\/wp-json\/wp\/v2\/tags?post=44920"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}