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  WINTER CAMP LECTURE NOTES Ozgur KircakNovember 29, 2010  2  Contents 1 NUMBER THEORY 5 1.1 DIVISIBILITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.1.1 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . 61.1.2 SOLUTIONS . . . . . . . . . . . . . . . . . . . . . . . . . 71.2 PRIME AND COMPOSITE NUMBERS . . . . . . . . . . . . . . 121.2.1 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . 121.2.2 SOLUTIONS . . . . . . . . . . . . . . . . . . . . . . . . . 131.3 SQUARES AND CUBES . . . . . . . . . . . . . . . . . . . . . . 171.3.1 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . 171.3.2 SOLUTIONS . . . . . . . . . . . . . . . . . . . . . . . . . 181.4 REPUNITS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211.4.1 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . 211.4.2 SOLUTIONS . . . . . . . . . . . . . . . . . . . . . . . . . 22 2 ALGEBRAIC EXPRESSIONS 25 2.1 SOME USEFUL IDENTITIES . . . . . . . . . . . . . . . . . . . 252.2 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262.3 SOLUTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3 QUADRATICS 37 3.1 QUADRATIC EQUATIONS . . . . . . . . . . . . . . . . . . . . 373.1.1 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . 383.1.2 SOLUTIONS . . . . . . . . . . . . . . . . . . . . . . . . . 423.2 SYSTEMS OF QUADRATIC EQUATIONS . . . . . . . . . . . . 573.2.1 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . 573.2.2 SOLUTIONS . . . . . . . . . . . . . . . . . . . . . . . . . 583.3 QUADRATIC FUNCTIONS . . . . . . . . . . . . . . . . . . . . 613.3.1 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . 613.3.2 SOLUTIONS . . . . . . . . . . . . . . . . . . . . . . . . . 633.4 QUADRATIC INEQUALITIES . . . . . . . . . . . . . . . . . . . 653.4.1 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . 653.5 IRRATIONAL EQUATIONS-INEQUALITIES . . . . . . . . . . 683  4 ¬†CONTENTS¬† 4 COMPLEX NUMBERS 71 4.1 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 5 TRIGONOMETRY 75 5.1 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 6 LOGARITHM 79 6.1 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
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