Find all pairs of positive integers \( a \) and \( b \) such that \( a | (b^2 + b + 1) \) and \( b | (a^2 + a + 1) \).
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2016-15 Pair of integers,
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Find all pairs of positive integers \( a \) and \( b \) such that \( a | (b^2 + b + 1) \) and \( b | (a^2 + a + 1) \).