Find all pairs x, y, such that x3 y and y3 x are divisible by x2 y2 Find all values of a for which equation ex2 ax always has exactly two roots

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Find all pairs x, y, such that x3 + y and y3 + x are divisible by x2 + y2. Find all values of a

Find all pairs x, y, such that x3 + y and y3 + x are divisible by x2 + y2. Find all values of a for which equation ex2 = ax always has exactly two roots.

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