Helping Solve Mathematics Competition Problems Using Computer Technology

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Hao Shi


The International Mathematical Olympiad (IMO) is the World Championship Mathematics Competition for High School students and is held annually in a different country. The competition paper consists of six problems from various areas of secondary school mathematics, broadly classifiable as geometry, number theory, algebra, and combinatorics. Finding the solutions to these problems requires contestants’ exceptional mathematical ability and excellent mathematical knowledge. In order to identify mathematical talents, many countries organise annual national mathematics competitions. Some countries develop a systematic approach to nurture their talents via a series of enrichment training programs. In our research, we focus on one specific area of mathematics competition problems at a time, especially the problem challenge to computer. We regard this paper as the first introductory paper for our further ‘Human vs Computer’ research into assisting solving mathematics competition problems using computer technology. In this paper, we concentrate on ‘find last digits of a number’ as part of number theory. First a brief introduction of IMO is presented. Second the normal human solutions to the ‘last digits of a number’ are given. Then precision in Computer Science is explained in term of data types. Computer algorithm in pseudo code is present and function called FindLastDidgits is then developed in C#. Finally we develop Windows and Web applications using Microsoft Visual Studio to demonstrate that with assistance of Computer Technology, we can easily find last digits of an extremely large number with exponentiation. The developed generic utility can be used to validate the human solution in a systematic way.


Keywords: International Mathematical Olympiad (IMO); Mathematics Competition, Number Theory; Last Digits of a Number; Computer Technology; Precision; Programming; Windows Application; Web Interface.


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