题目

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:
|(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&#

提问时间：2021-03-01

答案