101 Problems in Algebra - MATHEMATICAL OLYMPIADS

101 PROBLEMS IN ALGEBRA

FROM THE TRAINING OF THE USA IMO TEAM

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AMT PUBLISHING

101 PROBLEMS IN ALGEBRA

FROM THE TRAINING OF THE USA 1MO TEAM

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Published by AMT PUBLISHING Australian Mathematics Trust University of Canberra ACT 2601

AUSTRALIA

Copyright ?2001 AMT Publishing Telephone: +61 2 6201 5137

AMTT Limited ACN 083 950 341 National Library of Australia Card Number and ISSN Australian Mathematics Trust Enrichment Series ISSN 1326-0170

101 Problems in Algebra ISBN 1 876420 12 X

THE AUSTRALIAN MATHEMATICS TRUST

ENRICHMENT S E R I E S

EDITORIAL COMMITTEE

Chairman Editor

GRAHAM H POLLARD, Canberra AUSTRALIA PETER J TAYLOR, Canberra AUSTRALIA

WARREN J ATKINS, Canberra AUSTRALIA ED J BARBEAU, Toronto CANADA GEORGE BERZSENYI, Terra Haute USA RON DUNKLEY, Waterloo CANADA WALTER E MIENTKA, Lincoln USA NIKOLAY KONSTANT1NOV, Moscow RUSSIA ANDY Liu, Edmonton CANADA JORDAN B TABOV, Sofia BULGARIA JOHN WEBB, Cape Town SOUTH AFRICA

The books in this series are selected for their motivating, interesting and stimulating sets of quality problems, with a lucid expository style in their solutions. Typically, the problems have occurred in either national or international contests at the secondary school level.

They are intended to be sufficiently detailed at an elementary level for the mathematically inclined or interested to understand but, at the same time, be interesting and sometimes challenging to the undergraduate and the more advanced mathematician. It is believed

that these mathematics competition problems are a positive

influence on the learning and enrichment of mathematics.

THE AUSTRALIAN MATHEMATICS TRUST

ENRICHMENT SERIES

BooKs IN THE SERIES

1 AUSTRALIAN MATHEMATICS COMPETITION BOOK 1 1978-1984 JD Edwards, DJ King Et PJ O'Halloran

2 MATHEMATICAL TOOLCHEST

AW Plank Et NH Williams

3 TOURNAMENT OF TOWNS QUESTIONS AND SOLUTIONS 1984-1989 PJ Taylor

4 AUSTRALIAN MATHEMATICS COMPETITION BOOK 2 1985-1991 PJ O'Halloran, G Pollard Et PJ Taylor

5 PROBLEM SOLVING VIA THE AMC W Atkins

6 TOURNAMENT OF TOWNS QUESTIONS AND SOLUTIONS 1980-1984

PJ Taylor

7 TOURNAMENT OF TOWNS QUESTIONS AND SOLUTIONS 1989-1993 PJ Taylor

1 8 ASIAN PACIFIC MATHEMATICS OLYMPIADS 1989-2000 H Lausch Et C Bosch Giral

9 METHODS OF PROBLEM SOLVING BOOK 1 JB Tabov Ft PJ Taylor

10 CHALLENGE! 1991-1995 JB Henry, J Dowsey, AR Edwards, U Mottershead, A Nakos Et G Vardaro

ii USSR MATHEMATICAL OLYMPIADS 1989-1992

AM Slinko

1 12 AUSTRALIAN MATHEMATICAL OLYMPIADS 1979-1995

H Lausch Et PJ Taylor

13 CHINESE MATHEMATICS COMPETITIONS AND OLYMPIADS 1981-1993 A Liu

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