Maths Olympiad Exam

Prove that the product of the first 200 positive even integers differs from the product of the
first 200 positive odd integers by a multiple of 401.

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Maths Olympiad Other Question

If x, y, z are the sides of a triangle, then prove that
|x^2(y - z) + y^2(z - x) + z^2(x - y)| < xyz. In an acute triangle ABC, points D, E, F are located on the sides BC, CA, AB respectively
such that
CD*CE=CA*CB, AE*AF=AB*AC, BF*BD=BC*BA.
Prove that AD, BE, CF are the altitudes of ABC.