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| 來自：ywsing0 | 時間：Wed Jan 25 13:35:04 2006 | | o殊, 慢慢做. | | <table width=750><tr><td>1. pythagorean number is a set of three integers: a, b, c which staisfy following condition. | a<sup>2</sup> + b<sup>2</sup> = c<sup>2</sup> | write a program to list all of the pythagorean number up to 1000 | (Use C,C++,C#, Java or BASIC) | | 2. consider a pair of two positive integers (m,n) which satisfy following two conditions | 7m+3n = 10<sup>2004</sup> | n/m is integer | how many pairs of such two integers exist? | | 3. There are n positive variables A<sub>1</sub>, A<sub>2</sub>, A<sub>3</sub>, ...A<sub>n</sub>. Consider A that is the minimum value of following numbers | A<sub>1</sub> / (1+A<sub>1</sub>), A<sub>2</sub> / (1+A<sub>1</sub>+A<sub>2</sub>), ... A<sub>n</sub> / (1+A<sub>1</sub>+A<sub>2</sub>+...+A<sub>n</sub>) | What becomes of maximum value of A when each variable changes meeting the following condition? | A<sub>1</sub> + A<sub>2</sub> + A<sub>3</sub> + ... + A<sub>n</sub> = 1 | | 4. There are two figures on the same plane. one is an equilateral triangle OAB whose length of one side equals 1 and the other is a line m, which passes point O but does not cross side AB. And A' and B' are cross points between line m and altitudes to m each from A and B. Calculate maximum value of AA' + BB'.</tr></td></table>
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