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Find all pairs of (x, y) of positive integers such that 2x +7y divides 7x + 2y.

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Let d = gcd (x, y). Then x = dx1 and y = dy1. We observe that 2x + 7y divides 7x + 2y if and only if 2x1 + 7y1 divides 7x1 + 2y1. This means 2x1 + 7y1 should divide 49x1 + 14y 1. But 2x1 + 7y1 divides 4x1 + 14y1. Hence 2x1 + 7y1 divides 45x1. Similarly, we can show that 2x1 + 7y1 divides 45x1. Hence 2x1 + 7y1 divides gcd(45x1, 45y1) = 45gcd(x1, y1) = 45. Hence

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