Maths Olympiad Exam

If n is an integer greater than 7, prove that
n^7-hn^7 is divisible by 7. Here n^7 denotes the number of ways of choosing 7 objects from among n objects; also, for any real number x, [x] denotes the greatest integer not exceeding x.

Read Solution (Total 0)

Maths Olympiad Other Question

Let ABC be a triangle in which AB = AC and CAB = 90◦. Suppose M and
N are points on the hypotenuse BC such that BM2 + CN2 = MN2. Prove that
MAN = 45◦. Let a, b, c be three positive real numbers such that a + b + c = 1. Prove that among the three numbers a - ab, b - bc, c - ca there is one which is at most 1/4 and there is one which is at least 2/9