The USSR Olympiad Problem Book: Selected Problems and Theorems of Elementary Mathematics [3 ed.]
Over 300 challenging problems in algebra, arithmetic, elementary number theory and trigonometry. Complete solutions. 196
498 163 4MB
English Pages 242 Year 1993
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Citation preview
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THE USSROLYMPIAD PROBLEM BOOI(
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SelecteclProblemsancl Theorems of ElementaryMathematics
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D.O.Shklarsky,N.N.Chentzov, and l.M.Yaglom This book contains 320 unconventional number theory and trigonometry.
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in algebra, arithrnctic, clcrntntary of tht' problt'rrrs first appe:rrecl in competitive examinations sponsorerd by thc School Matht'rrratit':rl Sot'it'ty of thc Moscow State University and in the Matlrcnratical ()lyrnpilrls hckl in Most.orv. Although most of the problems presupp()s('orrly lriglr st lrool rnlrllrt'rrrrtit's, tlrt'y rrrt' not easy; some are of uncommon difficrrlty :rrrrl will clrrlL'rrgc tlrc irrgt'nrrity ol irny researchmathematician.Nevertheless,nrirrry:rrcrvr'll rvillrirrllrrr';rtlrol rrroIir':rlctl high school students and even advanct:rl scvcrrth :rrrtl t.iglrtlr {r:r,k'rs.
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scr'li.rrs Arr,rrr11 llrtsr';rrr': llrt The problems are grouped into twclvt's('l):lr:lll divisibility of integers, equati