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Chapter 1 1.8 BMO 2001 1.17 Russia MO 2002 Chapter 2

2.4 Viorel Vâjâitu, Alexandra Zaharescu, Gazeta Matematic˘a 2.15 Ireland MO 2000

Chapter 3

3.6 IMO, shortlist 1969 (Romania) 3.8 India MO 2003 Chapter 4 4.1 France MO 1996 4.3 South Africa MO 1995 4.7 Crux Mathematicorum 4.8 Sefket Arslanagic 4.10 Art of problem solving 4.11 Art of problem solving 4.13 Andrei Ciupan, Romania 2007 4.15 Crux Mathematicorum 4.20 Pham Kim Hung Corollary 4.5: Walther Janous Chapter 5

5.3 IMO, shortlist 1974 (Finland) 5.10 Zdravko Cvetkovski 5.13 Zdravko Cvetkovski 5.14 Zdravko Cvetkovski 5.15 Zdravko Cvetkovski

Z. Cvetkovski, Inequalities,

DOI10.1007/978-3-642-23792-8, © Springer-Verlag Berlin Heidelberg 2012

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Chapter 6 6.2 IMO 1975

6.4 IMO 1964 (Hungary) 6.6 IMO 1995

6.10 Song Yoon Kim Chapter 8

8.1 Darij Grinberg 8.2 Poland MO 1999 8.3 Calin Popa

8.4 Walther Janous, Crux Mathematicorum 8.6 APMO 2004

Chapter 9

9.1 Singapore MO 2002 9.2 Sefket Arslanagic 9.6 Le Viet Thai 9.7 Pham Kim Hung 9.8 Pham Kim Hung

9.10 Walther Janous, Crux Mathematicorum Chapter 10

10.5 Zdravko Cvetkovski 10.6 Zdravko Cvetkovski 10.7 Zdravko Cvetkovski 10.11 Nguyen Manh Dung Chapter 12 12.5 Darij Grinberg 12.7 APMO 2004 12.10 IMO 1984 12.11 IMO 1995 Chapter 14 14.2 Iran MO 1996 14.6 United Kingdom 1999 Chapter 15 15.2 Vietnam TST 1996 15.3 Vietnam 2002 15.4 Darij Grinberg Chapter 17 17.2 IMO 2005

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Chapter 18

18.3 Pham Kim Hung

18.5 Nguyen Minh Duc, IMO shortlist 1993 Chapter 20

6 Titu Andreescu, TST 2001 USA 9 Russia 2002

12 Czech and Slovak Republics 2005 14 Walther Janous, Crux Mathematicorum 16 Vasile Cîrtoaje, Gazeta Matematic˘a 20 Titu Andreescu, Gabriel Dospinescu 22 Art of problem solving

23 Vasile Cîrtoaje 28 Art of problem solving 33 Art of problem solving 36 Belarus 1996

37 Art of problem solving 40 Zdravko Cvetkovski 41 Zdravko Cvetkovski 42 Zdravko Cvetkovski

45 Mircea Lascu, Gazeta Matematic˘a 48 Art of problem solving

49 IMO 2000, Titu Andreescu 50 Bulgaria, 1997

56 Baltic Way, 2005

57 Gabriel Dospinescu, Marian Tetiva 58 Adrian Zahariuc

68 Vasile Cîrtoaje 71 MOSP 2001

72 Vasile Cîrtoaje, Mircea Lascu, Junior TST 2003 Romania 73 Marian Tetiva

75 Latvia 2002 81 Peru 2007 82 Romania 2003 84 Art of problem solving 86 Japan 2005

88 Art of problem solving 90 Canada 2008

91 Mathlinks contest 97 Kiran Kedlaya

98 Zdravko Cvetkovski, shortlist JBMO 2010 99 Vasile Cîrtoaje, Gazeta Matematic˘a 105 JBMO 2002, shortlist

110 Pham Kim Hung 113 Pham Kim Hung

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115 Pham Kim Hung 117 Zdravko Cvetkovski 118 Macedonia MO 1999 119 Zdravko Cvetkovski 125 Pham Kim Hung

126 Titu Andreescu, USAMO 2004 129 MYM, 2001

131 Vietnam 136 Vietnam, 1998

139 Zdravko Cvetkovski, BMO shortlist 2010 144 IMO, shortlist 1996 (Slovenia)

154 Nguyen Van Thach 156 Pham Kim Hung

160 Dinu ¸Serbanescu, Junior TST 2002, Romania 161 Zdravko Cvetkovski, Macedonia MO 2010 162 Pham Kim Hung

163 Romania 2008 165 IMO, shortlist 1987 166 JBMO, 2003 167 Pham Kim Hung

170 Florina Cârlan, Marian Tetiva 173 Darij Grinberg

176 Art of problem solving 179 Art of problem solving 184 Ukraine MO 2004 188 JBMO 2002, shortlist

190 IMO, shortlist 1990 (Thailand) 191 Titu Andreescu, Mircea Lascu 195 Poru Loh, Crux Mathematicorum 196 Pham Kim Hung

197 Moldova TST 2005 198 IMO shortlist 1994

199 IMO shortlist 1998 (Russia) 200 IMO shortlist 1993 (USA) 202 IMO, shortlist 1968 (Poland) 207 China MO 1996

212 IMO, shortlist 1992 (Great Britain) 213 A. Teplinsky, Ukraine MO 2005

214 Daniel Campos Salas, Mathematical Reflections 2007 217 Cezar Lupu, Romania MO 2005

218 Titu Andreescu, USAMO 2001

219 Gabriel Dospinescu, Mircea Lascu, Marian Tetiva 237 IMO 1961 (Poland)

250 Zdravko Cvetkovski

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264 Pham Kim Hung

265 Mihai Piticari, Dan Popescu 271 Art of problem solving 280 Tran Nam Dung 281 Le Trung Kien 287 Zdravko Cvetkovski

288 Vasile Cîrtoaje, Gazeta Matematic˘a 292 Serbia 2008

294 Vasile Cîrtoaje, Gazeta Matematic˘a 298 Pham Kim Hung

300 Art of problem solving 302 Art of problem solving 303 Art of problem solving 304 India 2002

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APMO Asian-Pacific Mathematical Olympiad BMO Balkan Mathematical Olympiad IMO International Mathematical Olympiad JBMO Junior Balkan Mathematical Olympiad MYM Mathematics and Youth magazine, Vietnam MO Mathematical Olympiad

MOSP Mathematical Olympiad Summer Program

USAMO United States of America Mathematical Olympiad

Z. Cvetkovski, Inequalities,

DOI10.1007/978-3-642-23792-8, © Springer-Verlag Berlin Heidelberg 2012

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1. Agahanov, H.X.,i dr.:Vserossiskie Olimpiady Xkolnikov po Matematike

1993–2006.MCNMO,Moskva(2007) (Agakhanov, N.H., et al.: All-Russian Olympic in

Mathematics 1993–2006, MCNMO, Moscow, 2007)

2. Alfutova,B.N.,Ustinov, A.B.:Algebra i Teori Qisel dl Matematiqeskih Xkol.MCNMO,Moskva(2003) (Alfutova, B.N., Ustinov, A.V.: Algebra and Number

Theory for Mathematical Schools, MCNMO, Moscow, 2003)

3. Andreescu, T., Enescu, B.: Mathematical Olympiad Treasures. Birkhäuser, Basel (2003) 4. Andreescu, T., Cirtoaje, V., Dospinescu, G., Lascu, M.: Old and New Inequalities. Gil

Pub-lishing House, Zalau (2004)

5. Andreescu, T., Feng, Z., Lee, G.: Mathematical Olympiads 2000–2001; Problems and Solu-tions from Around the World. Math. Assoc. of America, Washington (2001)

6. Arslanagiˇc, Š.: Matematika za Nadarene. Bosanska Rijeˇc, Sarajevo (2005) (Mathematics for Gifted Students, Bosanska Rijeˇc, Sarajevo, 2005)

7. Arslanagiˇc, Š.: Metodiˇcka Zbirka Zadataka sa Osnovama Teorije iz Elementarne Matematike. Grafiˇcar promet, Sarajevo (2006) (Methodical Collection of Problems with the Basic Theory of Elementary Mathematics, Grafiˇcar promet, Sarajevo, 2006)

8. Art of Problem solving:http://www.artofproblrmsolving.com

9. Bottema, O., et al.: Geometric Inequalities. Wolters-Noordhoff Publishing, Groningen (1969) 10. Dimovski, D., i dr.: Praktikum po Elementarna Matematika. Prosvetno

delo, Skopje (1993). (Dimovski, D., et al.: Practicum for Elementary Mathematics.

Prosvetno delo, Skopje (1993))

11. Djuki´c, D., Jankovi´c, V., Mati´c, I., Petrovi´c, N.: The IMO Compendium, a Collection of Prob-lems Suggested for the International Mathematical Olympiad: 1959–2004, 1st edn. Springer, Berlin (2006)

12. Engel, A.: Problem-Solving Strategies. Springer, New York (1997)

13. Hardy, G.H., Littlewood, J.E., Pólya, G.: Inequalities. Cambridge University Press, Cambridge (1967)

14. Iboldin,O.,Kurlandqik,L.:Neravenstvo Iencena.Kvant4, 7–10 (2000).

(Izboldin, O., Kurlandcik, L.: Jensen’s inequality. Quant 4, 7–10 (2000)) 15. Kedlaya, K.S.:A < B,http://www.unl.edu.com

16. Kim Hung, P.: The stronger mixing variables method. Math. Reflect. 6, 1–8 (2006) 17. Kim Hung, P.: Secrets in Inequalities, vol. 1. Gil Publishing House, Zalau (2007) 18. Larson, C.L.: Problem Solving Through Problems. Springer, New York (1983)

19. Lee, H.: Topics in Inequalities—Theorems and Techniques. The IMO Compendium Group (2007)

20. Li, Y.K.: Math Problem Book I. Hong Kong Mathematical Society (2001) 21. Lozanski, E., Rousseau, C.: Wining Solutions. Springer, New York (1996) Z. Cvetkovski, Inequalities,

DOI10.1007/978-3-642-23792-8, © Springer-Verlag Berlin Heidelberg 2012

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22. Malqeski, P.,Malqeski, A.:Izbrani sodrini od elementarna matematika. SDMI,Skopje(1994) (Malcheski, R., Malcheski, A.: Selected Content from Elementary

Mathematics, SDMI, Skopje 1994) 23. MathLinks:http://www.mathlinks.ro

24. Matic, I.: Classical Inequalities. The IMO Compendium Group (2007)

25. Nomirovski,D:Neravenstvo Karamaty.Kvant4, 43–45 (2000). (Nomirovski, D.:

Karamata’s inequality. Quant 4, 43–45 (2000))

26. Prasolov, B.B.:Zadaqi po algebre, arifmetike i analizu(2005) (Prasolov, V.V.:

Problems in Algebra, Arithmetic and Analysis, 2005)

27. Puong, T.: Diamonds in Mathematical Inequalities. HaNoi Publishing House (2007) 28. Sedrakn,N.:O primenenii odnogo neravenstva.Kvant2, 42–44 (1997).

(Se-drakian, N.: For the usage of recent inequality. Quant 2, 42–44 (1997))

29. Shklarsky, D.O., Chentzov, N.N., Yaglom, I.M.: The USSR Olympiad Problem Book. Dover, New York (1994)

30. Slinko, A.: USSR Mathematical Olympiads 1989–1992. Australian Mathematical Trust, Bel-connen (1997)

31. Verdiyan, V., Salas, D.C.: Simple trigonometric substitutions with broad result. Math. Reflect. 6, 1–12 (2007)

References

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