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今回の動画ではr+のfで時々出現する周期性による矛盾を用いた単射を示す補題とAPMO2023P4の解説をしました。 難易度は3~4程度だと思います。 10:人間には不可能問題 公式の別解はこちらからどうぞ https://apmo-official.org/static/solu...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3152071/86d35cb47c72eb2b8b4b46fa99b93b05/564x318_1"},"target":"_self","position":"3","reqid":"1764373961905973-13343544629080032437-balancer-l7leveler-kubr-yp-sas-153-BAL","summary":{"fullTextUrl":"/int_search_summary?data=http%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DMNf2Ulv_Pu0","linkTemplate":"/video/preview/17618612052622055390?parent-reqid=1764373961905973-13343544629080032437-balancer-l7leveler-kubr-yp-sas-153-BAL&text=%E6%9F%8F%E9%99%BD%E9%AB%98%E6%A0%A1%E6%95%B0%E5%AD%A6%E9%83%A8%EF%BC%88%E5%AE%9F%E8%B3%AA%E3%83%91%E3%82%BD%E3%82%B3%E3%83%B3%E9%83%A8%EF%BC%89&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Apmo2023年p4の関数方程式の解説【Function equations of the Mathematics 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Thanks for watching. Please also go to the links below. チャンネル運営と動画制作を支援していただけると幸いです。 -- いものリスト:https://www.amazon.co.jp/hz/wishlist/... (ちなみに同じカートに入れて決済すると好きな...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/1607438/2d09ee082e31593d67b1397fe0eea23c/564x318_1"},"target":"_self","position":"5","reqid":"1764373961905973-13343544629080032437-balancer-l7leveler-kubr-yp-sas-153-BAL","summary":{"fullTextUrl":"/int_search_summary?data=http%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DuD7U_wYMl2M","linkTemplate":"/video/preview/16682089934185387788?parent-reqid=1764373961905973-13343544629080032437-balancer-l7leveler-kubr-yp-sas-153-BAL&text=%E6%9F%8F%E9%99%BD%E9%AB%98%E6%A0%A1%E6%95%B0%E5%AD%A6%E9%83%A8%EF%BC%88%E5%AE%9F%E8%B3%AA%E3%83%91%E3%82%BD%E3%82%B3%E3%83%B3%E9%83%A8%EF%BC%89&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"高校数学vs大学数学","related_orig_text":"柏陽高校数学部(実質パソコン部)","related_porno":false,"related_less_3m_off":true,"client":"d2d","no_cnt":1,"related_src":"serp","related":"{\"porno\":false,\"vfp\":1,\"orig_text\":\"柏陽高校数学部(実質パソコン部)\",\"url\":\"http:\\/\\/www.youtube.com\\/watch?v=uD7U_wYMl2M\",\"src\":\"serp\",\"rvb\":\"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_Q4E-gf9AuoD_Pr6__8A8gD5DgUC_wDgDAP5_f4AAPQPCAD7AAAAAQgB_vH-AQAOAgb8_AAAAPvr-vn_AQAAAAf9AP4BAAD4DwAEA_8AABb7AQX0_gEA_g4GCgEAAAATE_z4AQAAAPjh-_wBAAAAIAAtrT7ROzgTQAlITlACKnMQABpgUTUAFytlH_AgBubx7Q4y8PjO67nTE_805f8S7fn0B_ABtAr-_xj279mjAAAADtzZFvEA1n8tDaYx_A_KpakE6EF0AVYUPAspD84VRtcPFDrzKejpAN_3vPYDAjkeJuhAIAAtP9MZOzgTQAlIb1ACKq8GEAwaoAYAAFxCAACgQQAAdEIAACDCAADIwQAArkIAAJxCAAAQQQAAWMIAAFTCAADAQQAAHEIAAKDBAAAIQgAAhkIAAPDBAAAgQQAAoEAAAEBCAAAIQgAAQEEAAPjBAABYwgAAYEIAAKBBAAAYwgAAgMEAABjCAAAQwQAAmEIAAEDAAAAwQQAAoMEAABBBAACiwgAAqEEAAGDBAADWQgAAYEEAALBBAABgQgAAAEAAAIC_AABAQQAAVEIAALDBAADwQQAA8EEAAIRCAACEQgAAQMEAABDCAABAwAAAgD8AADjCAACawgAAnMIAAEBCAABwQQAAUEIAACBBAABQwQAAhsIAACjCAABwwQAA4MEAAJrCAAA8wgAAmMEAAGzCAAC4QQAA0EEAAJhBAACIQgAAUEEAAHDCAACgwgAABEIAADRCAACYQQAAsMEAABxCAADIQQAA2MEAAMDAAACcQgAAiEEAAMjBAABQQQAAQEEAAIC_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_AADaQgAAHMIAAIA_AACIwQAAQMEAAMjBAAC4wQAA0EEAABBCAAD4wQAAmEEAAEDAAADYwSAAOBNACUh1UAEqjwIQABqAAgAAcL0AABC9AACqPgAALD4AAAy-AACoPQAAhr4AAN6-AACAOwAAyD0AAGQ-AADgPAAAQLwAABw-AAC4vQAADL4AAHw-AADgvAAA-L0AAHA9AAB_PwAAiL0AAAS-AABEPgAAdL4AAKi9AAAwvQAAcL0AAKg9AACAuwAAUD0AAIA7AADIvQAAyD0AADC9AAAsvgAAcD0AANi9AABsvgAABL4AADQ-AAAMvgAAED0AADC9AADYvQAAuL0AAII-AACYPQAAuL0AABy-AAAQPQAAMD0AAJY-AACgPAAAdL4AAOA8AAAfPwAA4DwAAIC7AADIPQAA-L0AAOi9AABwPQAAoDwgADgTQAlIfFABKo8CEAEagAIAAGy-AADovQAAcL0AALq-AACGPgAAFD4AAIY-AADCPgAA2L0AADA9AAAwPQAABD4AAKA8AADgvAAAqL0AAFA9AAAsvgAAIz8AAI6-AACgPAAA2D0AAEC8AAAQvQAAgDsAAKC8AACgvAAAuL0AAMi9AAAkPgAAgDsAAIg9AACIvQAAJL4AAIg9AAAkPgAAJL4AAKI-AABMvgAAPL4AAMg9AABUPgAAdL4AAII-AABQPQAAJD4AADS-AAB_vwAAHD4AADA9AADgvAAAuD0AAIo-AADCPgAABL4AAFQ-AABAPAAAcL0AAIK-AAD4PQAAXD4AAKi9AAAcvgAAsr4AAIC7IAA4E0AJSHxQATAJOAFKAGAAaAA,\"}","related_url":"http://www.youtube.com/watch?v=uD7U_wYMl2M","parent-reqid":"1764373961905973-13343544629080032437-balancer-l7leveler-kubr-yp-sas-153-BAL","related_vfp":1,"relatedVideo":"yes"},"cwidth":1280,"cheight":720,"cratio":1.77777,"dups":["16682089934185387788"],"episode":0,"season":0,"isEmbedOnly":false,"greenHost":"YouTube","hasTranslation":true,"contentTypeId":null,"censored":false},"14902542340001834865":{"videoId":"14902542340001834865","docid":"34-9-15-ZE4460A12E4BC6462","description":"部活での活動記録です。 味を占めて二回目 今回の動画ではr+での補題とbmo2022の関数方程式の解説をしました。 動画の最後に演習問題が付いてるので時間がある人は是非見てみてください In this video, I explained the lemmas in R+ and the functional equations from BMO 2022. 本選4~5番級 7:IMO...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/491717/41ec396b758709a0d985e7328d79f01e/564x318_1"},"target":"_self","position":"6","reqid":"1764373961905973-13343544629080032437-balancer-l7leveler-kubr-yp-sas-153-BAL","summary":{"fullTextUrl":"/int_search_summary?data=http%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DmdZHQk62j-8","linkTemplate":"/video/preview/14902542340001834865?parent-reqid=1764373961905973-13343544629080032437-balancer-l7leveler-kubr-yp-sas-153-BAL&text=%E6%9F%8F%E9%99%BD%E9%AB%98%E6%A0%A1%E6%95%B0%E5%AD%A6%E9%83%A8%EF%BC%88%E5%AE%9F%E8%B3%AA%E3%83%91%E3%82%BD%E3%82%B3%E3%83%B3%E9%83%A8%EF%BC%89&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"[数オリ]非常に面白いbmoの関数方程式 – [Balkan Mathematical Olympiad 2022]","related_orig_text":"柏陽高校数学部(実質パソコン部)","related_porno":false,"related_less_3m_off":true,"client":"d2d","no_cnt":1,"related_src":"serp","related":"{\"porno\":false,\"vfp\":1,\"orig_text\":\"柏陽高校数学部(実質パソコン部)\",\"url\":\"http:\\/\\/www.youtube.com\\/watch?v=mdZHQk62j-8\",\"src\":\"serp\",\"rvb\":\"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_cIAQME_gH1Bu_5-P38APb6-_z-A_8A6fb5-Qn_AAD6EPD_AwAAAP7-_v_4_gAAJ_32_QEAAAAUAPMD_wAAAPgMAQX-AQAA9gsI_QMAAAATCggB_wAAAA4I-QD__wAABAkEBAAAAAAL9QUNAAAAACAALYiXzjs4E0AJSE5QAipzEAAaYAMdAB8JKBzYDAfv8QILBfX16_H16_4ACvMADfwK5AcM8t_5FQD67Q362AAAAAQM_BwHAM8z_gXq9hnp9wjm_QUVf_IoCQkRC_PhKBLm_Rcf9__c8gAFCvACHgnsHwj-KiAALXS_jTs4E0AJSG9QAiqvBhAMGqAGAABcQgAA2EEAAHhCAAAYwgAAoEEAAMhBAACaQgAAAMIAAPjBAADIQQAA2EEAAFTCAACQwQAAAAAAANhBAABQQQAAHEIAAITCAAC4QgAACMIAADzCAAAAwAAAXMIAAEBBAAAIwgAAaMIAADDBAABowgAAAEIAAGDBAAB8wgAA-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-AAD2vgAAQDwAADA9AABsPgAAQLwAAIC7AACIPQAAJL4AAOi9AAAkPgAAQLwAAJi9AAAcPgAAfz8AAJg9AAAkvgAAqD0AAIi9AAAsvgAAML0AABC9AADYPQAAqD0AADA9AABwvQAA6L0AAHA9AABAvAAA6L0AAIg9AAAQvQAARL4AAGS-AACgvAAAQLwAAIA7AAD4vQAALL4AAHS-AABEPgAAyD0AAOi9AAAsvgAA4LwAAPg9AAAkPgAAqD0AAJK-AAAwvQAA_j4AAKC8AABQPQAADD4AANi9AACgPAAA2D0AAEA8IAA4E0AJSHxQASqPAhABGoACAAAkvgAAPD4AAKA8AAAXvwAAML0AALg9AACIPQAAVD4AAKC8AACGPgAA-L0AAEA8AABwvQAAoLwAAAS-AACAuwAARL4AABk_AABsvgAALD4AAKi9AABcvgAAUL0AANi9AADgvAAAXD4AACy-AACgvAAAcD0AADA9AAAwvQAAQDwAABC9AAAwvQAAML0AAOC8AACePgAAyL0AAOC8AABQvQAAoDwAANi9AACgvAAA4DwAAKC8AACGvgAAf78AABQ-AACIvQAAij4AAMg9AACYPQAAVD4AAEQ-AACAuwAAgDsAAIi9AAA8vgAAuL0AABQ-AACYPQAABL4AADA9AAAwPSAAOBNACUh8UAEwCTgBSgBgAGgA\"}","related_url":"http://www.youtube.com/watch?v=mdZHQk62j-8","parent-reqid":"1764373961905973-13343544629080032437-balancer-l7leveler-kubr-yp-sas-153-BAL","related_vfp":1,"relatedVideo":"yes"},"cwidth":1280,"cheight":720,"cratio":1.77777,"dups":["14902542340001834865"],"episode":0,"season":0,"isEmbedOnly":false,"greenHost":"YouTube","hasTranslation":true,"contentTypeId":null,"censored":false},"7526325953399590924":{"videoId":"7526325953399590924","docid":"34-2-16-Z1DC08FCC44F13DDE","description":"ついに16.90まで来ました.あと0.1です....やばい Ai Cかなりの確率で抜けるので噛み合うまで時間がかかりました。 今回は精度意識してないのでかなりアタックが出てしまってます(悲しい)...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/2953774/fbacb57cfb6c692cbf4520abb70b8ca0/564x318_1"},"target":"_self","position":"7","reqid":"1764373961905973-13343544629080032437-balancer-l7leveler-kubr-yp-sas-153-BAL","summary":{"fullTextUrl":"/int_search_summary?data=http%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DWLQSiY4Vr5o","linkTemplate":"/video/preview/7526325953399590924?parent-reqid=1764373961905973-13343544629080032437-balancer-l7leveler-kubr-yp-sas-153-BAL&text=%E6%9F%8F%E9%99%BD%E9%AB%98%E6%A0%A1%E6%95%B0%E5%AD%A6%E9%83%A8%EF%BC%88%E5%AE%9F%E8%B3%AA%E3%83%91%E3%82%BD%E3%82%B3%E3%83%B3%E9%83%A8%EF%BC%89&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Road to 17.00 Ai C [Master 14+] SSS(FC)[Chunithm 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曲 「紅葉愛唄」(くれはいとしうた) • 紅葉愛唄 [Kureha Itoshiuta] / GARNiDELiA ... 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