{"app":{"locale":"en-GB"},"problem":{"content":"

Let a_n be the largest real root of a polynomial g(x) = x³ - 2ⁿ·x² + n.
For example, a₂ = 3.86619826...

Find the last eight digits of $\\sum \\limits_{i = 1}^{30} {\\left \\lfloor a_i^{987654321} \\right \\rfloor}$.

Note: $\\lfloor a \\rfloor$ represents the floor function.

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