Titlebook: Mathematical Olympiad Treasures; Titu Andreescu,Bogdan Enescu Textbook 2012Latest edition Springer Science+Business Media, LCC 2012 Algebr

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Number Theory and CombinatoricsMany Olympiad problems refer to arrays of numbers. Let us start with some examples.

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Algebra.?Factor (.+2.?3.).+(.+2.?3.).+(.+2.?3.)....?Observe that (.+2.?3.)+(.+2.?3.)+(.+2.?3.)=0. Because .+.+.=0 implies ..+..+..=3., we obtain

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Geometry and Trigonometry.?Let . be a convex quadrilateral. Prove that..?Let . be the point of intersection of the diagonals . and .. We have .+.>. and .+.>.; thus .+.>.+.. Similarly, .+.>. and .+.>.; thus .+.>.+.. It follows that. For the second inequality, note that .<.+. and .<.+.; hence. Analogously,. and the result follows by adding these inequalities.

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professors and?Mathematical Olympiad coaches, the text will be invaluable to teachers, students, and puzzle enthusiasts. The advanced reader is challenged to find alternative solutions and extensions of the proposed problems. .978-0-8176-8253-8

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