Maths Olympiad Exam

Find all primes p and q such that p^2 + 7pq + q^2 is the square of an integer.

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p=q=any prime
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Maths Olympiad Other Question

Let BE and CF be the altitudes of an acute triangle ABC, with E on AC and F on AB. Let O be the point of intersection of BE and CF. Take any line KL through O with K on AB and L on AC. Suppose M and N are located on BE and CF respectively, such that KM is perpendicular to BE and LN is perpendicular to CF. Prove that FM is parallel to EN. Find the number of positive integers x which satisfy the condition
h x
99 i = h x
101 i.
(Here [z] denotes, for any real z, the largest integer not exceeding z; e.g. [7/4] = 1.)