Maths Olympiad Exam

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◦.

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Maths Olympiad Other Question

Find all integers a, b, c, d satisfying the following relations:
(i) 1 a b c d;
(ii) ab + cd = a + b + c + d + 3. 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.