1.For which prime numbers p and q (if any),is 5p^2q + 16pq^2 a perfect square?2.Let C1,C2,C3,...,C2009 be a sequence of real numbers such that |Cn − Cn+1| is less or equal to 1 for 1 is less or equal to n is less or equal to 2008.Show that:\x0c

1.For which prime numbers p and q (if any),is 5p^2q + 16pq^2 a perfect square?2.Let C1,C2,C3,...,C2009 be a sequence of real numbers such that |Cn − Cn+1| is less or equal to 1 for 1 is less or equal to n is less or equal to 2008.Show that:\x0c
1.For which prime numbers p and q (if any),is 5p^2q + 16pq^2 a perfect square?
2.Let C1,C2,C3,...,C2009 be a sequence of real numbers such that |Cn − Cn+1| is less or equal to 1 for 1 is less or equal to n is less or equal to 2008.Show that:\x0c\x0c\x0c\x0c
|(C1+C2+...+C2009)/2009 − (C1+C2+...+C2008)/2008| is less or equal to 1/2.
3.Let ABC be a right-angled triangle with right angle at C.Pick a point D on the segment BC.Let E be a point on the circumcircle w of ABD,such that DE is perpendicular to AB.
Prove that angle BAE = angle BEA if and only if AC is tangent to w.
4.Let n greater or equal to 3 be an odd integer.Determine the maximum possible value of the sum:
square root of |X1 − X2| + square root of |X2 − X3| + · · · + square root of |Xn−1 − Xn| + square root of |Xn − X1|
where 0 is less or equal to Xi is less or equal to 1 for i = 1,2,...,n.
5.Determine the minimum possible value of the expression |n^2−5^(4m+3)| for non-negative integers m and n.
6.Michael’s mother likes to keep him busy with an odd form of solitaire.To set up the game she places coins on some of the squares of a normal 8×8 chessboard.Michael plays by adding one coin at a time,always placing coins only on squares which already have at least two adjacent squares containing coins.(Two squares are adjacent if they share an edge,but not if they only
share a vertex.)
Michael wins when he’s placed a coin on every square of the board.What is the minimum number of coins that Michael’s mother can place on the board to start with,so that it is still
possible for Michael to win?
m 和 n 是整数而且不是负数
|n^2−5^(4m+3)| 的最小值是什么？

1.For which prime numbers p and q (if any),is 5p^2q + 16pq^2 a perfect square?2.Let C1,C2,C3,...,C2009 be a sequence of real numbers such that |Cn − Cn+1| is less or equal to 1 for 1 is less or equal to n is less or equal to 2008.Show that:\x0c
1 .对于这种素数p和q （如有的话） ,是5p ^季度+ 16pq平方公尺一个完美的广场?
2 .让我们的C1 ,C2 ,补体C3 ,...,C2009是一个真正的序列号码这样|繁-雨蛙+ 1|小于或等于1为1小于或等于n是较少或等于2 008年.结果表明：
| （的C1 + C2 +...+ C2009 ） / 2009 -（的C 1+ C 2+ ...+C 2008） / 2 008|小于或等于1 / 2 .
3 .让美国广播公司是一个直角三角直角在角选择一个点D对部分公元前.设E是一个点的外接圆瓦特的阿卜杜拉,这样,德国是垂直于AB公司.
证明,英国宇航=角角BEA公司当且仅当交流是相切的瓦特
4 .设n大于或等于3是一个奇怪的整数.决定尽最大可能价值的总和：
平方根| X1 -X 2| +平方根| X 2-的X 3 |+ +平方根|差分-1 -差分| +平方根|差分- X1 |
其中0小于或等于少喜或等于1更多i = 1 ,2 ,...,注
5 .确定最低可能值的表达| ñ 2-5 ^ ^ （ 400 3 ） |的非负整数m和北
6 .迈克尔的母亲喜欢让他忙于一个奇怪形式的纸牌.要建立游戏金币的地方,她的一些广场的正常8 × 8棋盘.迈克尔起到了增加一个硬币的时间,总是把硬币只能在广场已经至少有两个相邻方载硬币.（二广场毗邻,如果它们共享的优势,但如果他们只
共用一个顶点.）
迈克尔赢得当他把一枚硬币的每平方米的董事会.什么是最低数目的硬币,迈克尔的母亲可以放置在董事会开始,所以这仍是
可能迈克尔的胜利吗?

1.prime number质数。……………………
只能把原题给你翻译过来，不一定能帮助你做，呵呵，看起来有难度。呵呵。

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