Maths Olympiad Exam

Find all functions f : R + R such that
f(x + y)f(x - y) = f(x) + f(y)
2 - 4x^2f(y), (1)
for all x, y - R, where R denotes the set of all real numbers.

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Maths Olympiad Other Question

Let ABCD be a quadrilateral inscribed in a circle. Let E, F, G, H be the midpoints of the arcs AB, BC, CD, DA of the circle. Suppose AC· BD = EG · FH. Prove that AC, BD, EG, FH are concurrent. Call a natural number n faithful, if there exist natural numbers a < b < c such that a divides
b, b divides c and n = a + b + c.
(i) Show that all but a finite number of natural numbers are faithful.
(ii) Find the sum of all natural numbers which are not faithful.