TY - BOOK AU - Andreescu,Titu AU - Dospinescu,Gabriel TI - Problems from the book SN - 9780979926907 U1 - 510 23 PY - 2008/// CY - Allen, TX PB - XYZ Press KW - Mathematics KW - Problems, exercises, etc N1 - Includes bibliographical references and index; 1. Some useful substitutions -- 2. Always Cauchy-Schwarz ... --- 3. Look at the exponent -- 4. Primes and squares -- 5. T2's lemma -- 6. Some classical problems in extremal graphy theory -- 7. Complex combinatorics -- 8. Formal series revisited -- 9. A brief introduction to algebraic number theory -- 10. Arithmetic properties of polynomials -- 11. Lagrange interpolation formula -- 12. Higher algebra in combinatorics -- 13. Geometry and numbers -- 14. The smaller, the better -- 15. Density and regular distribution -- 16. The digit sum of a positive integer -- 17. At the border of analysis and number theory -- 18. Quadratic reciprocity -- 19. Solving elementary inequalities using integrals -- 20. Pigeonhole principle revisited -- 21. Some useful irreducibility criteria -- 22. Cycles, paths, and other ways -- 23. Some special applications of polynomials N2 - Presents beautiful results, intriguing problems, and ingenious solutions. The problems range from elementary gems to deep truths. A truly delightful and highly instructive book, this will prepare the engaged reader not only for any mathematics competition they may enter but also for a lifetime of mathematical enjoyment ER -