Maths Olympiad Exam

Find all natural numbers n > 1 such that n2 does not divide (n - 2)!.

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Maths Olympiad Other Question

Let ABC be a triangle with circum circle. Let M be a point in the interior of triangle ABC which is also on the bisector of A. Let AM, BM, CM meet in A1, B1, C1 respectively. Suppose P is the point of intersection of A1C1 with AB; and Q is the point of intersection of A1B1 with AC. Prove that PQ is parallel to BC. Find all non-zero real numbers x, y, z which satisfy the system of equations:
(x^2 + xy + y^2)(y^2 + yz + z^2)(z^2 + zx + x^2) = xyz,
(x^4 + x^2y^2 + y^4)(y^4 + y^2z^2 + z^4)(z^4 + z^2x^2 + x^4) = x^3y^3z^3.