ኗ 㘆 ࡎ ㇉
ዣ 㙣 ㈤ 枼6$ 5DPDQXMDQ 枼6ULQLYDVD $L\DQJDU 1887
12 ᗙ 22 ᔐύᓴࣾတ㙣Ⴧዣᓫ₶୭᳇ᵺୖࣣ⻂ٔⵞ ೩ .XPEDNRQDP 枼7DQMRUH GLVWULFW 枼0DGUDV SURYLQFH 㑪 カ◵Ⴑ (URGH 柋1920 4 ᗙ 26 ᔐ࣯ᓴࣾတ㙣Ⴧዣᓫ 0DGUDV 㑪カᶣᕱᶣ &KHWSXW ώᓄฎ ώ
ዣ㙣㈤לݴⷍध㐩 7KH 0DF7XWRU +LVWRU\ RI 0DWKH PDWLFV DUFKLYH ┐⌴
?iiT,ffrrr@;`QmTbX/+bXbi@M/X+XmFf?BbiQ`vfSB+i.BbTHvf_KMmDMX?iKH
ኗ 㘆 ࡎ ㇉
㔉 ت ᅂ
ᭇॠ⌋ጦⲣ᷹⊣
ዣ 㙣 ㈤ 枼6$ 5DPDQXMDQ 枼6ULQLYDVD $L\DQJDU 1887
12 ᗙ 22 ᔐύᓴࣾတ㙣Ⴧዣᓫ₶୭᳇ᵺୖࣣ⻂ٔⵞ ೩ .XPEDNRQDP 枼7DQMRUH GLVWULFW 枼0DGUDV SURYLQFH 㑪 カ◵Ⴑ (URGH 柋1920 4 ᗙ 26 ᔐ࣯ᓴࣾတ㙣Ⴧዣᓫ 0DGUDV 㑪カᶣᕱᶣ &KHWSXW ώᓄฎ ώ
ፕ㛦ࣿ㊣ῳᕧ६ႃ⃞تݗ⽁⎔⃞݅ഄථ♭㒋ᔢ⃞ວႉ 栾ڒ ᖺ㒆 栾ㆧᙌࡒݗკკ цڒ⃞ᷫⶏᖺتວယၺ⃞✓ੌ 栾ᔉࡏᄴ
⪇ цࡑວ⛐ࡘجণڂ 栾㖫ڒᙋ 20 ℛ⃞⪩ᧃῳ᪃ цፕ㛦
ࣿ㊣ٯ᤺㒑൝ذ 栾⻗٦ࡒၣᄞ 栾ܨॖࡏ⼽ۄዑⷙ൘⃞ف
અᙀ ц1897 ၣ 栾९ڒ॒᤺ᗆ 栾ாࢩ┙⛑⸂فুࢧࡑᴼᷱ॑
⏜تু цڒᤱऑ➧⏱ላક㙃 цᙌتᤄ 栾ڒ⃞⛐ဳ⺋⸵⺋ࢲ㕦⃞
ᆄ⽶ 桌³㕦ⳝک۟ᔷ㔀 栾࡚ᄣᔷ㕦 ц´ ፕ㛦ࣿ㊣ᄣᙌٲ‹
ᇸ 栾ܨ⎫⾨܊ક⛐ဳ 桌³㕦ⳝ㕦㔀ᖺسᖺٜᄣ㕦"´ ㅚᗆ 栾ᔷ⃞
ംഹᆄ⽶ထდ⾨٦ڒ⃞ᩆሣ ц
॒٩᤺ᗆ 栾㞖⃞ীݩ═ڒتᙥᙖࡐ /RQH\ ໎⃞ъد
ы7ULJRQRPHWU\ 栾ڒா⇎ᗆ㒙ⴂ⠇ຌࡑᙀ 栾ؿⶫ⏹ᙀفዷ ᙌ⃞ક㙃 栾ㆧẺ⎧Ᏸ㊟⃞ᔷࡕ
eix = FRVx + iVLQx ц
1903 ၣ 栾ڒㅛㅻف⏜تᤄ࢛㉂⛑⸂ 栾ㅪࡏ⼽ۄዑⷙ൘ࡕ⎧
㓾⚫ цா㓾ழᙀ㚭 栾ڒݩࢲ॥ᷱ &DUU ⃞ъ┓ⓔᔷ៷ы 6\QRSVLV RI HOHPHQWDU\ UHVXOWV LQ SXUH PDWKHPDWLFV цㅚᖺتᙥ⢿
ᕄ᷹ᔢᙿ 栾ᙀف㔉ㄼ٦ 6000 ೬ݗࡕ 栾ےၬْㇺᨈᙌ⺯ᖣ цᄨ 1903 ၣࢲ 1907 ၣ 栾ፕ㛦ࣿ㊣ڐ┨⇩⻗ㅚᙥᙀ 栾⺯ᖣؿᏰႵ٦ᙀ
ف⃞╁ᚶ ц1904 ၣ 栾ڒஙᔷ⏯⸵⌫⚫◯ࠣ‥Ểᄣ㓾⃞Ẩ
㊣ 栾ၣ┸ 栾ங⢿⸩⏯⌋◯س۷⛘ᏖẨ㊣ цᙆᄞ 栾খ ஙᕄ⌋⛑⸂◯ဎᙣ❫ॖ┙ 栾ⳝㄹفㅖヘ цڒா㛦ᄹፕᕞ
⃞تዷ㓾⚫٦⇎ᘍ⃞تᥧᗆ㒙 栾࡚ᄞখㄬ⼽ዑⷙ൘ࡕ⎧
㓾 栾ےஙދ⌋খᙣ❫“ ц
⠇ 1907 ၣࢲ 1911 ၣ 栾ڒتΩᨈᙌதຖ⃞✓ 栾ےῳ᪃⃞
سຊຖؿس❫܃ڒᔷ⃞⠜⿄⌭ᬕ цㅚᥧᗆᙛ 栾ڒ⇩⍭٦ၩ
ᕥ хㅤ࢛ᔷ х⾰ၬ۟┙ᔷ х⽶ᔷਘ়ᔷ хᢐல⍕࢛⏯ цڒጮ
⇩⍭ᄣ⃞╁⹐ⷒ㍻ா⏬ⷒᙥذ цၬၣر܊ 栾⏬ⷒᙥⷒ٦⿏⿏د ೲᙥ цㅚٲᔷ╁⹐ㇺᨈᙌ═⺯ᖣㅻ⌫ ц
1909 ၣ 栾ፕ㛦ࣿ㊣╁ල 栾⸑ళ ຊ㛦 -DQNL $PPD ‧ᗆ ጁٚ᤺ цວڞᄞ 栾ᅃ㘙೩ῳ ц1910 ၣ 栾ڒጆ✖ࢲ⧏㟹ዑ ڳℛᷱ 7LUXNR\LOXU تݗ㏶⃞㏶㒆 5 ⡭ٳᷱ $L\DU ᖺتݗᔷ
ሬദ⛓ 栾سٍࣆㆧࣝ⎧٦६ႃᔷᙈ цፕ㛦ࣿ㊣့⦰⠇တ⃞
⇩⍭ᚶঔጤڒ 栾❫ᙌتڪⓝণ⃞ဎ܃ ц⡭ٳᷱ 6 㓨
ٳ $D\DU ၛࣾㄔἱ ц㓨ٳᙄᖺፕ㛦ࣿ㊣⃞⛐ဳ цாڒㆽⴂ 栾ፕ
㛦ࣿ㊣ጤࢲتڪڜἱࡕकੌ⃞ဉۦ цސ٦ၬݗᙋ 栾ڒখⳝڍ┯═
5 ፕഔ 5DR цፕഔᖺ㛦ᄹፕᕞڞऻ 150 ࡕ㊞⃞ࡐᩨᷱᕥ⃞ᄷ ᔉੌ 栾ᔷᄚᙌ⠜⿄ 栾ٜᖺ६ႃᔷᙈ⃞ࣝჃڂِت цፕ 㛦ࣿ㊣⛊㒑ᐄ⇿٦⃞⏬ⷒᙥ 栾ڒⶫ⸲⠇တ⃞ᔷ⃘Ἢ цፕഔ॒
࢛ቾሀㅚݗၣハڂ⃞ጁ❫ 栾ؿ⸟⻣ڒၨㄔ٨ੌ⃞ဉۦس❫ⶫ㔀 ڒ⃞㦦ᵧ цڒፕ㛦ࣿ㊣ࢲ㛦ᄹፕᕞঔ 栾ؿ㙌ሣᎃᗆ═ڒتٲ
㎓ 栾▂ڒتᥧᗆᙛ⃞ῳ᪃ 栾ীᗆᙌ㓊ᕥ㖭ፕ㛦ࣿ㊣ᷧঝ⇩
⍭ᩮ⽓ 栾ڞ܃ڒ❫ຊᅂᄨ٨⇩⍭ ц
تೳ 栾ፕ㛦ࣿ㊣≈ࢲتۗ⛐ᙎঙ ц⹅ࢲڒ⃞⇩⍭ဉۦᗆ 栾ㅚ
ۗ⛐ᙎঙڒ⸲ 桌³ڂݜ⍄⻩۪ᙌᔷ⃞ೳጁ´ ፕ㛦ࣿ㊣✖٦⏊
ㆀ 桌³ೳጁ" ⹈۪ℷℷዘ⃞✨´ ڒ✨ذ⃞⟈খ㦲খঅ цڒ ⶫ㊝ڒᖃ೭ா⇔ذⷆ␡ 栾Ό⇿ယ܊ᓎ⇔ذ⃞⢔ᗆ㒙 栾ᕧ
ᖺၬ࢛㐿Ό✨ΩᏮᓎ⇔ذ⃞ цᙎঙકڒᖁᵃۦㅚ㦧೬ⷆ␡
۟سΌ┘܊໎" ፕ㛦ࣿ㊣⸲ڒㅤস㚉ㇺક㙃 栾ⴂᙌ㎓ঔ⽎ㅚ 㦧೬⃞┘ ц
উ܊ 栾⇩⍭ᩮ⽓ᨈ❫ ⹈ࢲጀ 栾ፕ㛦ࣿ㊣খس㙌ሣࢭڂ╲
ᱢذ⃞भⳟ 栾ထᙌتݗᙋᨈࢲፕഔㆽⴂঔ፼㎓٦ цၧദ╲ፕഔঘ
࡚ڒڂڍ┯ 栾ڒᕧ 1912 ၣா㛦ᄹፕᕞᬦकጤࢲتڪဉۦ 栾ᙋ⪩
ᙋ 25 ℛ цா᪤ᬦ 栾ڒ╲္፻تٲभ⳿┘܊ސ⣾⍋ 栾ᙌᗆ ࢯΌဉ㒙ڹᆷாㄔࡕປⴂސⷆ␡ ц ᕧᅂسாᴨ 栾ڒᙄၬᤄጮ␡
⍋ாဉۦᕄڧفت⾨ㅉٷذ┙ 栾ሑتٲ㦦ᵧ цㅚᥧᗆᙛ 栾ፕ 㛦ࣿ㊣ாᔷذထࢩ㖔㘲 栾ாъ६ႃᔷᙈ㕖⸞ы-RXUQDO RI WKH ,QGLDQ 0DWKHPDWLFDO 6RFLHW\ ذ⃘ⲯ٦ڒ⃞⏜ت⹐ᕄ ³ۄࣿࢯᔷ
⃞تٲᆄ⽶´ 6RPH SURSHUWLHV RI %HUQRXOOL¶V QXPEHUV 栾⌭ᄞ 栾খ
⃘ⲯ٦تጟ㓊ᕧ┙ᔷ хᴸ⎔⍕ хπ ⃞ၬ۟ㄩیᠫㅡᕄ⎮ ц
ாتٲᙎঙ⃞㧠ऑر 栾ፕ㛦ࣿ㊣ᕧ 1913 ၣ 1 ᙋ 16 ᖃ═⢿மࣰ
ೲ⃞⦰ুᔷວ *+ ڜ +DUG\ ໎٦ت໙݅ 栾݅ف⹅ࢲڒ
⽶ᔷ࢛۔⃞⇩⍭ 栾ؿ㓬ذڒாহݗᔷ࢛ᔆف⃘Ἢ⃞ 120 ݗຖ ἱਘࡕ цㅚٲຖἱਘࡕㇺᨈᙌ═⺯ᖣㅻ⌫ цڜ⸟⅂໌ᛦ ٦ㅚٲ╁⹐ 栾⸟ፕ㛦ࣿ㊣ᖺتݗڂጁ 栾ܨঘᗆ═ڒ٦݅ 栾ㆣ ڒ܊ࣰت⾨ۦ⇩⍭ цۦ⬦⸪⃞ථ♭㒋ᔢᄡ 栾ፕ㛦ࣿ㊣㕛 㒑६ႃᙌዷ㙙ቦ цᕧᖺ 栾 㛦ᄹፕᕞೲڒຊᏞ٦ࡒၣ⃞Ẩ
㊣ 栾ڞܚڒᄨ٨ᔷ⇩⍭ ц
ڜ㘤ᙘ 栾ےڎ☟☪ᤴጤᢍᙈ цᤳദڒ⃞تݗী٨
(+ ࡐ▂ᷱ 1HYLOOH ா㛦ᄹፕᕞ⺋ 栾ڜ൦ⷑڒध⸲ㅚݗၣ
ハڂ 栾ᙆᄞ┸ᕧࣹ٦ ц1914 ၣ 栾ፕ㛦ࣿ㊣ᄨ६ႃ܊ࢲدت
㓾 栾ᄣࢲࣰೲ═٧⃞ᄚࠣঅ⃞Ẩ㊣ цڜਘ -( ᙽḚᷱ
ڵᄹ /LWWOHZRRG ڒຊᏞ٦تຖ⃞ㅪ݇⸵⌫ 栾ڞჳ⳾ڒாళ⊃
⇉⺼ذ⃞س⿏ цாڜਘᙽḚᷱڵᄹ⃞ၛࣾر 栾ڒ⃞⇩⍭ဉۦㅪ
།ㄢㅠ цாᤦ᩺⃞ٯၣⴂ 栾ڒா⢿ம хᨷம хᄹம⃞ᔷ㕖⸞
ذࡘ⃘ⲯ٦ 21 ⹐ᕄ ࡚فᙌၬᖺ⠛ڜ়ۦ⃞ 栾ᤴ೩ 栾ா
ъ६ႃᔷᙈ㕖⸞ыㆧ⃘ⲯ٦೬⹐ᕄ хⷤⷒ⏯ ц ᕧ⇩⍭ᚶफ़
⦰ 栾ፕ㛦ࣿ㊣ᕧ 1918 ၣⳝᏰ㆛⢿ம⃠ວᙈᙈੌঘدت㓾⃞
⇩⍭ੌ цㅚٲ᠕⻔ম⸲ᖺتݗᔷວᬫᙘ⃞ᙆ㞖᠕⻔ 栾⛘ፕ㛦ࣿ
㊣ாد॒᤺ညলᄣࢲ٦ 栾ㅚᖺݽᄣ⠇⼒⃞تᕥ㖭 цےᖺদتᕥ 㖭 栾 ᕧڒㅻႃघ┧ 栾ゎ㞓ٜㅡ٦تຖ⃞७ цখ ᕧڒᖺ
⬦⸪⃞ථ♭㒋ᔢᄡ 栾╆ഄⲟ┟㙿ى⚉ 栾ா⢿ம⃞ㅚᥧᗆᙛ 栾ڒ
◮ᖺ⠇တᵪ㙿 栾ظ္္ங⇩⍭⛘ᅏⷒস㚉 цㅚ܃ᄣڒ⃞ゎ㞓⾲
܊⾲⬪ფ 栾ᄞ܊╲္ሯࢲゎذᙌᴸু⃞⁑ 栾ᙆᄞጁ⃘Ἢᇕ٦㊟
⁙ 栾ম❫ᖺ✽╁ 栾ㅚᗆᖺ 1917 ၣ ц
ፕ㛦ࣿ㊣ா⢿ம⃞ᙆᄞتၣၬْࡑᖺா₵㚙㓾ႃㅻ⃞ 栾ےڒڎ ࡑࣸڞ⾦ᄨ٨ᔷ⇩⍭ цٜ⢿ம຺ࡶ⃞ᦶݤ✽⁙سࢯ 栾ഫ ᚶࢲ६ႃম❫ᙈᆪᄯޛ႒ цᕧᖺڒ᧳ຖம цے ᕧ⏜تᤄ غ‐ೲይ⃞ᄉ㘐 栾ڒتΩ㕜ڞⲟ 栾Ωࢲ 1919 ၣ 4 ᙋጁࢲ ६ႃ ц㛦ᄹፕᕞೲڒຊᏞ٦ٯၣᙛၣ 250 ⢿㏘⃞⇩⍭ᩮ
⽓ 栾ীᗆᓓᐋ፠ڒᔢᏕ ц
1920 ၣ 4 ᙋ 26 ᖃ 栾ፕ㛦ࣿ㊣⁙ㅞᕧ㛦ᄹፕᕞ 栾ၣߘد॒د
᤺ цڒتῳᬑ⽁ 栾ᄞߘ‖رࡒღᵥ᷸ 栾ڞঘتݗᶒᔶΌ⃞ᶒᧃ ⳇਘتٲᙀ⒗ᕄ⍋ цḚࢭݽᄣتᐋ⃞ᖺڒᴸᔷ⽁ዷຯ٧⃞
ᬂ࢜ীᇭਘ㓊ᅂ цڒா⢿ம⁙㊟ᗆ 栾ᙄ ڜ໎رڒণㄼ═㛦ᄹ ፕᕞೲ⃞݅ 栾⸋ೲ═٧⃞Ẩ㊣ۦഫر⃞ຊᏞ 桌
³㔀٦ت࢛═ዘວڂ೩ 栾ࣔ㚣⃞⹈Όாᔢ✹ᕥ㖭 栾ഫᬕ⎔
ڂዜࡁ⃞⽒ 栾⽒ܚ═ڒݜ⸵ᙥ ц· · · ·´
ῳسᆷ 栾ይ㟉سᤲ 栾ፕ㛦ࣿ㊣ா⠅┸ࣆ 栾ڎڞ㘠შ⃞ᥲࣸ
ㅪⲟᔷ⇩⍭ цᕧᖺ 栾ா㛦ᄹፕᕞ⃞⁙ذῳ٦ڒ⃞⏜கᙥ⏬
ⷒᙥ ц⸋⏬ⷒᙥⳝ⍄ ³㆝⃞⏬ⷒᙥ´ 栾ஙாڒᄞتΩس⇉
ر⦝ㆁٯ॒೬ၣ цΩࢲ 1976 ၣ 栾♶ம⽤೨ᨷٳೲᔢᏕ * ຊ
ᄹ㟹ᕞ $QGUHZV ⷛકࣰೲدت㓾ᗆ 栾ா⸋ᜉ⃞ழᙀ㚭ف⃘
Ἢ цㅚᙥ⏬ⷒᙥفभ⦰ 600 㚣ࡕ 栾ےㇺᨈ═⺯ᖣㅻ⌫ ц ڒ⃞ࣆدݗ⏬ⷒᙥထᕧ 1967 ၣ᷹ 栾³㆝⃞⏬ⷒᙥ´ ٜ ६
ႃ◮ἱᕧ 1987 ၣ 12 ᙋ 22 ᖃጟࡾࡕᕧغ цڒ⃞়㕃ထ ࣰೲ
᷹⊣᷹ цۦڒ⃞⓿ᅡ 栾㛦ᄹፕᕞೲჃ⎧⃞تݗ㞖⏯
ᔷ⇩⍭ዷ 栾ڞڒ⃞ুু ц
◢ፕ㛦ࣿ㊣⃞ᔷဉۦ 栾ೲ⠍মڞ࢛دݗᗆᙛ ц⏜تݗ ᗆᙛ 1907 ± 1911 ၣ 栾९ڒᴸதຖ✓⃞ㆽᥧᗆᙛ 桍⏜٩ݗ ᗆᙛ 1914 ± 1918 ၣ 栾९ڒா⢿மࣰೲ⃞ᗆᙛ 桍⏜دݗᗆ ᙛ 1919 ± 1920 ၣ 栾९ڒ⁙ㅞࣆتၣ цڒா⏜تݗᗆᙛ⃞ဉۦ ىⷒ㍻ாڒ⃞ࣆدݗ⏬ⷒᙥف ц࡚فೲ࢛ࡐຩभᴸ⎔┙
ᔷ хຖ⍕࢛ хۄࣿࢯᔷਘ γ ᔷ⏯೬╲╁ᚶ⃞㊟ᕟ⃘Ἢ 栾ㅚ ᡥ⸲ᖺ়ᇭ়ἱ⃞ ц㛘࠻ 栾تݗຖἱዜࡕ 栾ாسী⃞ᗆ㒙س
ী⃞㦼 سী⃞ڂẺ⎧⃘Ἢዜ⺯ᖣ 栾ㅚாᔷذᖺ༕س 㠟⃞ ц࡚ᤄ 栾ፕ㛦ࣿ㊣ঞࢲദၬၣ㞖⏯ᔢ✹ 栾㑿⇩٦㞖⏯ᔷ
⃞ళ⊃⇉⺼ ц॥ᷱ⃞ъ┓ⓔᔷ៷ы⏯ᙀ 栾㕐ᵃ♭ࢧ٦ت ೲఽࡕ 栾ᨈᙌ═⺯ᖣㅻ⌫ 栾॒࢛ᚺᶺᴸ 栾ےፕ㛦ࣿ㊣
܊⸲ 栾ॵટ⊡٦⇩⍭⃞⿾ᡞ цڒᖺῳ᪃ாت⍁⽁⎔⦝ᄞ⃞ᾦಓ ⴂ⃞⛓ 栾ᴸᨷᄣࢲ⓼╚⃞ᔷⷎ▸ዜᏮⶻダຌ⃞ழᙀ⽝
ᕍ 栾ᖺ㖫⦰ڒ⃞ᔚ㍁⃞ໂࣸਘΩࣸ хშई⃞ᅼ▂ࣸਘⷒኜ
ࣸ 栾ڞঘजചࢼ⢶⃞ⓙ⊾ 栾ㅚጁ܃ᄣڒ❫೮ސذㄼㆽٲ㊟ᕟ⃘
Ἢ цڒᄞ܊ዷސ⃞೬⇩⍭ 栾ٜ❫೮ாࣆدݗ⏬ⷒᙥف⃘Ἢݜ
⃞⿲ цᕧᖺ 栾ாፕ㛦ࣿ㊣ㅚⴂ 栾মڞℷࢲتٲسᤳ္⃞Ἢ
⼋ 栾ㅚㇺᖺ ᕧڒ⃞ᔷళ⊃ἱ⹐س೮┦້⛘ㅡ⃞ цഫ 栾ڒ ڞᡤᕥ⌫ਘⴜᔷٗᨷຖἱۦ⇩⍭ဉ࡛ 栾ॵᨈᙌ㕓ㅩᙛᔷ⃞៷ ᅡ 桍ڒ⇩⍭ⶫᚬᔷ⹐ 栾⛘ڒ⃞ⴜ⻝ᔷ៷ᅡॵᄚᡤⓝ цდΌڜ
⃞⸊⸲ 桌³ڒ⃞ᠫᔷ⺯ᖣ⃞៷ᅡᖺتٲᙆᡤⓝ⃞ᐊㄼ цڒ
⃞ࡑ╁ᚶ 栾ᕟ⃞ዜ⛐⃞ 栾⃞ዜ㎟⃞ 栾ㇺᖺ㖫⹐⺯ хΩঘ
┌⃞ᬈ়⬧ἱ⛘ㆁࢲ⃞ 栾࡚ف 栾ڒࡑㇺᙣ❫═ک۟㛘ت⠍
⃞⹐ᓆ ц´ ےᖺ 栾ᔷᖺت㒋ㆯャᆄ៰შ х⹐⺯៰ັ⃞⌋
栾ፕ㛦ࣿ㊣⃞ㅚ⍁Ḛຖ⃞㙣⠇ᵃڒ⃞⇩⍭ᙈ့܊تٲس⡣ᄉ 㘐 цഫ 栾ڒ⽶ᔷ࢛۔⃞⇩⍭࡚ஙㅚ⍁ფ㦼⛘⧙ঞᐳ цங
ᤴ 栾ᄨذㄼㅚ⍁ႃ܊ℷ 栾ڒ⃞ဉۦت⠴ᔷἱ⹐⃞⃘།⼽ỉ
`ᄴ ц
ᄞ܊ᔷວ⃞ဉۦᄉ㘐ダೲ⃞ᖺڒாᄞࡒݗᗆᙛ⃞⇩⍭ ц
࡚ى⇩⍭ᚶᖺாఽೈᔷ⹐ Ḛࢭᖺᔳᔷ࢛ፒἱ⹐ хᢐல
ᔷ х⾰ၬ۟ᔷ хᡤᔷ х⃘ᔧ┙ᔷ⏯ᕥ㖭 ц‧ᵃ 栾ഫࣆዷ ㄼ 栾ㅚ࡚فᙌ೬ဉۦٜ❫೮ாڒ⏜تݗᗆᙛ⃞⏬ⷒᙥفጤࢲ
ళ цڒாᤦ⃘᩺ⲯ⃞⏜ت⹐ᕄ ³ᡤᕥ⌫ਘ π ⃞ㄩی´ 0RGXODU HTXDWLRQV DQG DSSUR[LPDLRQV WR π 栾═٦ π ⃞೬Ḛ᥉⃞ᄚദ⃞
ㄩی 栾࡚فೲ࢛ᖺࢯΌၢᕥⲯ⃞ цڒ⃞㒆ⲣ⹐ᕄ ³㞖
়ᔷ´ +LJKO\ FRPSRVLWH QXPEHUV ᄉ㘐ダೲ 栾ᕄف⹐⺯٦㞖়
ᔷ⃞تٲ㊟ᆄ⽶ цா⠛ڜ়໎⃞ت⹐ᕄ ³ᔳᔷ n ⃞⽶ங⃞
ᔷ´ 7KH QRUPDO QXPEHU RI SULPH IDFWRUV RI D QXPEHU n ف 栾ፕ 㛦ࣿ㊣⇩⍭٦تݗᔳᔷ⃞⽶ங⃞ၢક㙃 ц
㓊ᕧᔳᔷ⃞࢛ᚬἱ⹐ᖺፕ㛦ࣿ㊣⼽ỉᙆೲ⃞تݗ㘥ఝ цڒாㅚ ᕥ㖭⃞ᚶᄞ܊ᔷວဉۦ⃞ᄉ㘐ダ࡚ᕥ㖭ٜᖺᙆೲ⃞ цڒ
⠛ڜா 1918 ၣ়໎⃞⹐ᕄ ³┺়࢛ᚬ⃞ᯧㄩࡕ´ $V\PSWRWLF IRUPXODH LQ FRPELQDWRU\ DQDO\VLV 栾⺯ᖣ٦ۅⷆ
An−1e2√n < P(n) < Bn−1e2√2n 栾
A хB ᛖࡒݗᤳ္ᔷ цؿ㛘࠻ᐋலᨷ 栾Ό⺯ᖣ٦ᯧㄩࡕ
P(n) ∼ (4√
3n)−1ec√n 栾
࡚ف c = π q2
3 ц+ ፕᄹ㛦⾞ᷱ 5DGHPDFKHU ᕧ 1937 ၣᄣࢲ┙ᔷ ⲯㆁ
P(n) = 1 π√
2 X∞
k=1
Ak(n)√ k d
dn
VLQK(cλnk−1) λ
栾
࡚ف λn = q
n − 241 хAk(n) ᖺᛖتᎁᔷਘ ц
ፕ㛦ࣿ㊣㓊ᕧᔳᔷ n ⃞࢛ፒᔷ P(n) ⃞ী㚣⃞⇩⍭ٜ℩
‧ু ц1919 ၣ 栾ڒڐ┨⇩⍭٦ 3$ 㦜࠽㛦ᩲ 0DF0DKRQ
▮ㅡ⃞ P(n) (n ≤ 200) ᔷݽⲯ 栾⃘Ἢㅚٲᔳᔷ⠛ᛖٲ⽶ᔷ
ঘ࡚ࡱী㚣 цڒࢯΌᢐலᔷἱ⹐ 栾⺯ᖣ٦تٲ╁ᚶ 栾ᄣࢲ٦ P(5n + 4) ≡ 0 (PRG5) хP(7n + 5) ≡ 0 (PRG7) хP(11n + b) ≡ 0 (PRG11) хP(25n + 24) ≡ 0 (PRG25) ⏯ 栾ؿᐋتݗẆላ 桌
⢵ 24λ ≡ 1 (PRG5a7b11c) 栾ࣁ
P(5a7b11cn + λ) ≡ 0 (PRG5a7b11c) (1) ٩॒غ⓿د॒ၣڜ 栾6 ৼፕ &KRZOD ᄨ + তᗣ *XSWD ▮ࢷ
⃞ᓚೲ⃞ P(n) ݽⲯف⃘Ἢ 桌㕐ᵃ 24 · 243 ≡ 1 (PRG73) 栾ےᖺ P(243) = 133978259344888 ≡ 0 (PRG73) ц
1938 ၣ 栾*% ᧺ទ :DWVRQ ⺯້٦ፕ㛦ࣿ㊣Ẇላ 1 ⃞݇ᤳ㙃
ዷᙌ 5 ਘ 7 ⃞ࡱᖺᤳ≌⃞ 栾1967 ၣ 栾$2/ 㓨Ḛ㊣ $WNLQ ⺯ ᖣ٦ 桌
⢵ 24λ ≡ 1 (PRG5a7b11c) 栾ࣁ
P(5a7b11cn + λ) ≡ 0 (PRG5a7[(b+2)/2]11c) ц
ذㄼম 栾ፕ㛦ࣿ㊣Ẇላ 1 ፟٦ᔳᔷ࢛ፒἱ⹐⇩⍭⃞㘥 ఝ 栾थ٦೬ᔷວ⃞⇩⍭ဉۦ ц
ፕ㛦ࣿ㊣ㆧ⃘Ἢؿ⺯ᖣ٦೬⠛ P(n) ⃞ী㚣ᆄᙌ㓊⃞ᆙ⏯
栾ഫ
P(4) + P(9)x + P(14)x2 + · · ·
= 5[(1 − x5) (1 − x10) (1 − x15)· · ·]5 [(1 − x) (1 − x2) (1 − x3)· · ·]5 ц ㅚݗᆙ⏯ⳝ⸟ᖺፕ㛦ࣿ㊣ᚶ⃞ᙆദڜⲯِت ц
ᒄ Ḃ
ࣕತᒄḂ
[1] 6 5DPDQXMDQ &ROOHFWHG SDSHUV RI 6 5DPDQXMDQ &DPEULGJH 8QLY 3UHVV /RQGRQ DQG 1HZ <RUN 1927 UHSULQWHG E\ &KHOVHD 1HZ <RUN ц
[2] *+ +DUG\ DQG 6 5DPDQXMDQ $V\PSWRWLF IRUPXODH LQ FRPEL QDWRU\ DQDO\VLV 3URF /RQGRQ 0DWK 6RF 171918 2 75 ± 115 ц
[3] 5DPDQXMDQ¶V OHWWHUV DQG UHPLQLVFHQFHV 0HPRULDO QXPEHU 9RO 1 HGLWHG E\ 3. 6ULQLYDVDQ 0XWKLDOSHW +LJK 6FKRRO 0DGUDV 1968 ц
[4] 7KH ORVW QRWH ERRN DQG RWKHU XQSXEOLVKHG ZULWLQJV RI 6ULQLYDVD 5DPDQXMDQ HGLWHG E\ *( $QGUHZV 1DURVD 3XEOLVKHUV1987 ц [5] 1RWHERRNV RI 6ULQLYDVD 5DPDQXMDQ 2 YROV %RPED\ 1957 ц
℠⊤ᒄḂ
[6] %& %HUQGW5DPDQXMDQ¶V QRWH ERRNV 6SULQJH±9HUODJ 1HZ <RUN 1985 ц
[7] *+ +DUG\ 5DPDQXMDQ 7ZHOYH OHFWXUHV RQ VXEMHFWV VXJJHVWHG E\ KLV OLIH DQG ZRUN &DPEULGJH 1940 ц
[8] 2 2UH 6ULQLYDVD $L\DQJDU 5DPDQXMDQ 'LFWLRQDU\ RI VFLHQ WLILF ELRJUDSK\ 9RO 11 1975 267 ± 269 ц
[9] -1 .DSXU 6ULQLYDVD 5DPDQXMDQ%LRJUDSKLFDO DQG KLVWRULFDO HVVD\V 9RO 7 0DWKHPDWLFDO 6FLHQFHV 7UXVW 6RFLHW\ 1HZ 'HOKL 1990 ц
[10] *( $QGUHZ 7KH WKHRU\ RI SDUWLWLRQV $GGLVRQ:HVOH\ /RQ GRQ 1976 ц
