Latest Maths Olympiad Aptitude Question SOLUTION: Find all primes p and q such that p^2 + 7pq + q^2 is the square of an integer.

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Previous 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. Next Question: 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.)

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Find all primes p and q such that p^2 + 7pq + q^2 is the square of an integer.: Asked In Maths Olympiad MAN (11 years ago); Unsolved Read Solution (1); Is this Puzzle helpful? (1) (2) Submit Your Solution

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Previous 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. Next Question: 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.)

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