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				<div style="text-align:left;margin-bottom:20px;">  		</div><span itemprop="name" class="title">The IMO Compendium<br></span><span class="subtitle">A Collection of Problems Suggested for The International Mathematical Olympiads: 1959-2009 Second Edition<br></span><p>Autoren:<br><span itemprop="author" class="author"><b>Dusan Djukic, Vladimir Jankovic, Ivan Matic, Nikola Petrovic</b></span></p><p>Verlag:<br><b itemprop="publisher">Springer-Verlag </b>&nbsp;&nbsp;<a onclick="SearchPublEnt(680)" href="#">Weitere Titel dieses Verlages anzeigen</a></p>		
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<span class="notbold">Auflage: </span>2nd Edition<br><span class="notbold">Erschienen: </span>Mai 2011<br><span class="notbold">Seiten: </span>809<br><span class="notbold">Sprache: </span>Englisch<br><span class="notbold">Preis: </span>85.59 €<br><span class="notbold">Illustration: </span>200 schwarz-weiße Abbildungen
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						<h1><a href="_9781441998538_inhalt.html">Inhaltsverzeichnis</a></h1>
						<p><table><tr><td>1</td><td>Introduction</td><td>I</td></tr><tr><td>1.1</td><td>The International Mathematical Olympiad</td><td>1</td></tr><tr><td>1.2</td><td>The IMO Compendium</td><td>2</td></tr><tr><td>2</td><td>Basic Concepts and Facts</td><td>5</td></tr><tr><td>2.1</td><td>Algebra</td><td>5</td></tr><tr><td>2.1.1</td><td>Polynomials</td><td>5</td></tr><tr><td>2.1.2</td><td>Recurrence Relations</td><td>6</td></tr><tr><td>2.1.3</td><td>Inequalities</td><td>7</td></tr><tr><td>2.1.4</td><td>Groups and Fields</td><td>9</td></tr><tr><td></td><td>2.2 Analysis....................................................................................Iq</td><td></td></tr><tr><td>2.3</td><td>Geometry</td><td>12</td></tr><tr><td>2.3.1</td><td>Triangle Geometry</td><td>12</td></tr><tr><td>2.3.2</td><td>Vectors in Geometry</td><td>13</td></tr><tr><td></td><td>2.3.3 Bary centers..............................................................................¡4</td><td></td></tr><tr><td>2.3.4</td><td>Quadrilaterals</td><td>14</td></tr><tr><td>2.3.5</td><td>Circle Geometry</td><td>15</td></tr><tr><td>2.3.6</td><td>Inversion</td><td>16</td></tr><tr><td>2.3.7</td><td>Geometric Inequalities</td><td>17</td></tr><tr><td>2.3.8</td><td>Trigonometry</td><td>17</td></tr><tr><td></td><td>2.3.9 Formulas in Geometry................................................................1§</td><td></td></tr><tr><td>2.4</td><td>Number Theory</td><td>19</td></tr><tr><td>2.4.1</td><td>Divisibility and Congruences</td><td>19</td></tr><tr><td>2.4.2</td><td>Exponential Congruences</td><td>20</td></tr><tr><td>2.4.3</td><td>Quadratic Diophantine Equations</td><td>21</td></tr><tr><td>2.4.4</td><td>Farey Sequences</td><td>22</td></tr><tr><td>2.5</td><td>Combinatorics</td><td>22</td></tr><tr><td>2.5.1</td><td>Counting of Objects</td><td>22</td></tr><tr><td>2.5.2</td><td>Graph Theory</td><td>23</td></tr><tr><td>3</td><td>Problems</td><td>27</td></tr><tr><td>3.1</td><td>IM0 1959</td><td>27</td></tr><tr><td>3.1.1</td><td>Contest Problems</td><td>27</td></tr><tr><td>3.2</td><td>IMO 1960</td><td>29</td></tr><tr><td>3.2.1</td><td>Contest Problems</td><td>29</td></tr><tr><td>3.3</td><td>IMO 1961</td><td>30</td></tr><tr><td>3.3.1</td><td>Contest Problems</td><td>30</td></tr><tr><td>3.4</td><td>IMO 1962</td><td>31</td></tr><tr><td>3.4.1</td><td>Contest Problems</td><td>31</td></tr><tr><td>3.5</td><td>IMO 1963</td><td>32</td></tr><tr><td>3.5.1</td><td>Contest Problems</td><td>32</td></tr><tr><td>3.6</td><td>IMO 1964</td><td>33</td></tr><tr><td>3.6.1</td><td>Contest Problems</td><td>33</td></tr><tr><td>3.7</td><td>IMO 1965</td><td>34</td></tr><tr><td>3.7.1</td><td>Contest Problems</td><td>34</td></tr><tr><td>3.8</td><td>IMO 1966</td><td>35</td></tr><tr><td>3.8.1</td><td>Contest Problems</td><td>35</td></tr><tr><td>3.8.2</td><td>Some Longlisted Problems 1959-1966</td><td>35</td></tr><tr><td>3.9</td><td>IMO 1967</td><td>41</td></tr><tr><td>3.9.1</td><td>Contest Problems</td><td>41</td></tr><tr><td>3.9.2</td><td>Longlisted Problems</td><td>41</td></tr><tr><td>3.10</td><td>IMO 1968</td><td>49</td></tr><tr><td>3.10.1</td><td>Contest Problems</td><td>49</td></tr><tr><td>3.10.2</td><td>Shortlisted Problems</td><td>49</td></tr><tr><td>3.11</td><td>IMO 1969</td><td>53</td></tr><tr><td>3.11.1</td><td>Contest Problems</td><td>53</td></tr><tr><td>3.11.2</td><td>Longlisted Problems</td><td>53</td></tr><tr><td>3.12</td><td>IMO 1970</td><td>61</td></tr><tr><td>3.12.1</td><td>Contest Problems</td><td>61</td></tr><tr><td>3.12.2</td><td>Longlisted Problems</td><td>62</td></tr><tr><td>3.12.3</td><td>Shortlisted Problems</td><td>68</td></tr><tr><td>3.13</td><td>IMO 1971</td><td>70</td></tr><tr><td>3.13.1</td><td>Contest Problems</td><td>70</td></tr><tr><td>3.13.2</td><td>Longlisted Problems</td><td>71</td></tr><tr><td>3.13.3</td><td>Shortlisted Problems</td><td>76</td></tr><tr><td>3.14</td><td>IMO 1972</td><td>79</td></tr><tr><td>3.14.1</td><td>Contest Problems</td><td>79</td></tr><tr><td>3.14.2</td><td>Longlisted Problems</td><td>79</td></tr><tr><td>3.14.3</td><td>Shortlisted Problems</td><td>83</td></tr><tr><td>3.15</td><td>IMO 1973</td><td>86</td></tr><tr><td>3.15.1</td><td>Contest Problems</td><td>86</td></tr><tr><td>3.15.2</td><td>Shortlisted Problems</td><td>87</td></tr><tr><td>3.16</td><td>IMO 1974</td><td>89</td></tr><tr><td>3.16.1</td><td>Contest Problems</td><td>89</td></tr><tr><td>3.16.2</td><td>Longlisted Problems</td><td>90</td></tr><tr><td>3.16.3</td><td>Shortlisted Problems</td><td>95</td></tr><tr><td>3.17</td><td>IM0 1975</td><td>97</td></tr><tr><td>3.17.1</td><td>Contest Problems</td><td>97</td></tr><tr><td>3.17.2</td><td>Shortlisted Problems</td><td>97</td></tr><tr><td>3.18</td><td>IMO 1976</td><td>100</td></tr><tr><td>3.18.1</td><td>Contest Problems</td><td>100</td></tr><tr><td>3.18.2</td><td>Longlisted Problems</td><td>100</td></tr><tr><td>3.18.3</td><td>Shortlisted Problems</td><td>105</td></tr><tr><td>3.19</td><td>IMO 1977</td><td>107</td></tr><tr><td>3.19.1</td><td>Contest Problems</td><td>107</td></tr><tr><td>3.19.2</td><td>Longlisted Problems</td><td>107</td></tr><tr><td>3.19.3</td><td>Shortlisted Problems</td><td>113</td></tr><tr><td>3.20</td><td>IMO 1978</td><td>116</td></tr><tr><td>3.20.1</td><td>Contest Problems</td><td>II5</td></tr><tr><td>3.20.2</td><td>Longlisted Problems</td><td>116</td></tr><tr><td>3.20.3</td><td>Shortlisted Problems</td><td>121</td></tr><tr><td>3.21</td><td>IMO 1979</td><td>124</td></tr><tr><td>3.21.1</td><td>Contest Problems</td><td>124</td></tr><tr><td>3.21.2</td><td>Longlisted Problems</td><td>125</td></tr><tr><td>3.21.3</td><td>Shortlisted Problems</td><td>132</td></tr><tr><td>3.22</td><td>IMO 1981</td><td>135</td></tr><tr><td>3.22.1</td><td>Contest Problems</td><td>135</td></tr><tr><td>3.22.2</td><td>Shortlisted Problems</td><td>I35</td></tr><tr><td>3.23</td><td>IMO 1982......................................'</td><td>138</td></tr><tr><td>3.23.1</td><td>Contest Problems</td><td>138</td></tr><tr><td>3.23.2</td><td>Longlisted Problems</td><td>139</td></tr><tr><td>3.23.3</td><td>Shortlisted Problems</td><td>144</td></tr><tr><td>3.24</td><td>IMO 1983</td><td>147</td></tr><tr><td>3.24.1</td><td>Contest Problems</td><td>147</td></tr><tr><td>3.24.2</td><td>Longlisted Problems</td><td>147</td></tr><tr><td>3.24.3</td><td>Shortlisted Problems</td><td>154</td></tr><tr><td>3.25</td><td>IMO 1984</td><td>158</td></tr><tr><td>3.25.1</td><td>Contest Problems</td><td>158</td></tr><tr><td>3.25.2</td><td>Longlisted Problems</td><td>158</td></tr><tr><td>3.25.3</td><td>Shortlisted Problems</td><td>165</td></tr><tr><td>3.26</td><td>IMO 1985</td><td>168</td></tr><tr><td>3.26.1</td><td>Contest Problems</td><td>168</td></tr><tr><td>3.26.2</td><td>Longlisted Problems</td><td>168</td></tr><tr><td>3.26.3</td><td>Shortlisted Problems</td><td>177</td></tr><tr><td>3.27</td><td>IMO 1986</td><td>181</td></tr><tr><td>3.27.1</td><td>Contest Problems</td><td>181</td></tr><tr><td>3.27.2</td><td>Longlisted Problems</td><td>182</td></tr><tr><td>3.27.3</td><td>Shortlisted Problems</td><td>188</td></tr><tr><td>3.28</td><td>IMO 1987............................................ ^</td><td>192</td></tr><tr><td>3.28.1</td><td>Contest Problems</td><td>192</td></tr><tr><td>3.28.2</td><td>Longlisted Problems</td><td>192</td></tr><tr><td>3.28.3</td><td>Shortlisted Problems</td><td>200</td></tr><tr><td>3.29</td><td>IMO 1988</td><td>203</td></tr><tr><td>3.29.1</td><td>Contest Problems</td><td>203</td></tr><tr><td>3.29.2</td><td>Longlisted Problems</td><td>204</td></tr><tr><td>3.29.3</td><td>Shortlisted Problems</td><td>212</td></tr><tr><td>3.30</td><td>IMO 1989</td><td>217</td></tr><tr><td>3.30.1</td><td>Contest Problems</td><td>217</td></tr><tr><td>3.30.2</td><td>Longlisted Problems</td><td>218</td></tr><tr><td>3.30.3</td><td>Shortlisted Problems</td><td>229</td></tr><tr><td>3.31</td><td>IMO 1990</td><td>234</td></tr><tr><td>3.31.1</td><td>Contest Problems</td><td>234</td></tr><tr><td>3.31.2</td><td>Longlisted Problems</td><td>235</td></tr><tr><td>3.31.3</td><td>Shortlisted Problems</td><td>245</td></tr><tr><td>3.32</td><td>IMO 1991</td><td>249</td></tr><tr><td>3.32.1</td><td>Contest Problems</td><td>249</td></tr><tr><td>3.32.2</td><td>Shortlisted Problems</td><td>249</td></tr><tr><td>3.33</td><td>IMO 1992</td><td>253</td></tr><tr><td>3.33.1</td><td>Contest Problems</td><td>253</td></tr><tr><td>3.33.2</td><td>Longlisted Problems</td><td>253</td></tr><tr><td>3.33.3</td><td>Shortlisted Problems</td><td>262</td></tr><tr><td>3.34</td><td>IMO 1993</td><td>266</td></tr><tr><td>3.34.1</td><td>Contest Problems</td><td>266</td></tr><tr><td>3.34.2</td><td>Shortlisted Problems</td><td>267</td></tr><tr><td>3.35</td><td>IMO 1994</td><td>271</td></tr><tr><td>3.35.1</td><td>Contest Problems</td><td>271</td></tr><tr><td>3.35.2</td><td>Shortlisted Problems</td><td>271</td></tr><tr><td>3.36</td><td>IMO 1995</td><td>275</td></tr><tr><td>3.36.1</td><td>Contest Problems</td><td>275</td></tr><tr><td>3.36.2</td><td>Shortlisted Problems</td><td>275</td></tr><tr><td>3.37</td><td>IMO 1996</td><td>280</td></tr><tr><td>3.37.1</td><td>Contest Problems</td><td>280</td></tr><tr><td>3.37.2</td><td>Shortlisted Problems</td><td>281</td></tr><tr><td>3.38</td><td>IMO 1997</td><td>286</td></tr><tr><td>3.38.1</td><td>Contest Problems</td><td>286</td></tr><tr><td>3.38.2</td><td>Shortlisted Problems</td><td>287</td></tr><tr><td>3.39</td><td>IMO 1998</td><td>291</td></tr><tr><td>3.39.1</td><td>Contest Problems</td><td>291</td></tr><tr><td>3.39.2</td><td>Shortlisted Problems</td><td>291</td></tr><tr><td>3.40</td><td>IMO 1999</td><td>295</td></tr><tr><td>3.40.1</td><td>Contest Problems</td><td>295</td></tr><tr><td>3.40.2</td><td>Shortlisted Problems</td><td>295</td></tr><tr><td>3.41</td><td>IMO 2000</td><td>300</td></tr><tr><td>3.41.1</td><td>Contest Problems</td><td>300</td></tr><tr><td>3.41.2</td><td>Shortlisted Problems</td><td>300</td></tr><tr><td>3.42</td><td>IMO 2001</td><td>304</td></tr><tr><td>3.42.1</td><td>Contest Problems</td><td>304</td></tr><tr><td>3.42.2</td><td>Shortlisted Problems</td><td>304</td></tr><tr><td>3.43</td><td>IMO 2002</td><td>308</td></tr><tr><td>3.43.1</td><td>Contest Problems</td><td>308</td></tr><tr><td>3.43.2</td><td>Shortlisted Problems</td><td>308</td></tr><tr><td>3.44</td><td>IMO 2003</td><td>312</td></tr><tr><td>3.44.1</td><td>Contest Problems</td><td>312</td></tr><tr><td>3.44.2</td><td>Shortlisted Problems</td><td>312</td></tr><tr><td>3.45</td><td>IMO 2004................................... 'i^ '</td><td>317</td></tr><tr><td>3.45.1</td><td>Contest Problems</td><td>317</td></tr><tr><td>3.45.2</td><td>Shortlisted Problems</td><td>318</td></tr><tr><td>3.46</td><td>IMO 2005</td><td>322</td></tr><tr><td>3.46.1</td><td>Contest Problems</td><td>322</td></tr><tr><td>3.46.2</td><td>Shortlisted Problems</td><td>322</td></tr><tr><td>3.47</td><td>IMO 2006...................................!</td><td>326</td></tr><tr><td>3.47.1</td><td>Contest Problems</td><td>326</td></tr><tr><td>3.47.2</td><td>Shortlisted Problems</td><td>326</td></tr><tr><td>3.48</td><td>IMO 2007</td><td>331</td></tr><tr><td>3.48.1</td><td>Contest Problems</td><td>331</td></tr><tr><td>3.48.2</td><td>Shortlisted Problems</td><td>332</td></tr><tr><td>3.49</td><td>IMO 2008</td><td>336</td></tr><tr><td>3.49.1</td><td>Contest Problems</td><td>335</td></tr><tr><td>3.49.2</td><td>Shortlisted Problems</td><td>337</td></tr><tr><td>3.50</td><td>IMO 2009</td><td>341</td></tr><tr><td>3.50.1</td><td>Contest Problems</td><td>341</td></tr><tr><td>3.50.2</td><td>Shortlisted Problems</td><td>341</td></tr><tr><td>4</td><td>Solutions</td><td>347</td></tr><tr><td>4.1</td><td>Contest Problems 1959</td><td>347</td></tr><tr><td>4.2</td><td>Contest Problems 1960</td><td>349</td></tr><tr><td>4.3</td><td>Contest Problems 1961</td><td>351</td></tr><tr><td>4.4</td><td>Contest Problems 1962</td><td>353</td></tr><tr><td>4.5</td><td>Contest Problems 1963</td><td>354</td></tr><tr><td>4.6</td><td>Contest Problems 1964</td><td>355</td></tr><tr><td>4.7</td><td>Contest Problems 1965</td><td>357</td></tr><tr><td>4.8</td><td>Contest Problems 1966.....................................'</td><td>359</td></tr><tr><td>4.9</td><td>Longlisted Problems 1967</td><td>361</td></tr><tr><td>4.10</td><td>Shortlisted Problems 1968 ...............................^ '</td><td>374</td></tr><tr><td>4.11</td><td>Contest Problems 1969</td><td>380</td></tr><tr><td>4.12</td><td>Shortlisted Problems 1970</td><td>383</td></tr><tr><td>4.13</td><td>Shortlisted Problems 1971..................................'</td><td>339</td></tr><tr><td>4.14</td><td>Shortlisted Problems 1972</td><td>396</td></tr><tr><td>4.15</td><td>Shortlisted Problems 1973</td><td>401</td></tr><tr><td>4.16</td><td>Shortlisted Problems 1974</td><td>407</td></tr><tr><td>4.17</td><td>Shortlisted Problems 1975</td><td>413</td></tr><tr><td>4.18</td><td>Shortlisted Problems 1976</td><td>418</td></tr><tr><td>4.19</td><td>Longlisted Problems 1977</td><td>422</td></tr><tr><td>4.20</td><td>Shortlisted Problems 1978</td><td>437</td></tr><tr><td>4.21</td><td>Shortlisted Problems 1979</td><td>445</td></tr><tr><td>4.22</td><td>Shortlisted Problems 1981</td><td>453</td></tr><tr><td>4.23</td><td>Shortlisted Problems 1982</td><td>461</td></tr><tr><td>4.24</td><td>Shortlisted Problems 1983</td><td>467</td></tr><tr><td>4.25</td><td>Shortlisted Problems 1984</td><td>476</td></tr><tr><td>4.26</td><td>Shortlisted Problems 1985</td><td>483</td></tr><tr><td>4.27</td><td>Shortlisted Problems 1986</td><td>491</td></tr><tr><td>4.28</td><td>Shortlisted Problems 1987</td><td>498</td></tr><tr><td>4.29</td><td>Shortlisted Problems 1988</td><td>508</td></tr><tr><td>4.30</td><td>Shortlisted Problems 1989</td><td>523</td></tr><tr><td>4.31</td><td>Shortlisted Problems 1990</td><td>537</td></tr><tr><td>4.32</td><td>Shortlisted Problems 1991</td><td>550</td></tr><tr><td>4.33</td><td>Shortlisted Problems 1992</td><td>563</td></tr><tr><td>4.34</td><td>Shortlisted Problems 1993</td><td>573</td></tr><tr><td>4.35</td><td>Shortlisted Problems 1994</td><td>585</td></tr><tr><td>4.36</td><td>Shortlisted Problems 1995</td><td>593</td></tr><tr><td>4.37</td><td>Shortlisted Problems 1996</td><td>606</td></tr><tr><td>4.38</td><td>Shortlisted Problems 1997</td><td>622</td></tr><tr><td>4.39</td><td>Shortlisted Problems 1998</td><td>636</td></tr><tr><td>4.40</td><td>Shortlisted Problems 1999</td><td>650</td></tr><tr><td>4.41</td><td>Shortlisted Problems 2000</td><td>664</td></tr><tr><td>4.42</td><td>Shortlisted Problems 2001</td><td>677</td></tr><tr><td>4.43</td><td>Shortlisted Problems 2002</td><td>691</td></tr><tr><td>4.44</td><td>Shortlisted Problems 2003</td><td>702</td></tr><tr><td>4.45</td><td>Shortlisted Problems 2004</td><td>715</td></tr><tr><td>4.46</td><td>Shortlisted Problems 2005</td><td>730</td></tr><tr><td>4.47</td><td>Shortlisted Problems 2006</td><td>742</td></tr><tr><td>4.48</td><td>Shortlisted Problems 2007</td><td>754</td></tr><tr><td>4.49</td><td>Shortlisted Problems 2008</td><td>765</td></tr><tr><td>4.50</td><td>Shortlisted Problems 2009</td><td>777</td></tr><tr><td></td><td>A Notation and Abbreviations</td><td>791</td></tr><tr><td></td><td>A.l Notation</td><td>791</td></tr><tr><td></td><td>A.2 Abbreviations</td><td>792</td></tr><tr><td></td><td>B Codes of the Countries of Origin</td><td>795</td></tr><tr><td></td><td>C Authors of Problems</td><td>797</td></tr><tr><td></td><td>References......................................................... ^5</td><td></td></tr><tr><td></td><td></td><td></td></tr></table></p>
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