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Algebra Difficulty 5.0 AIME, harder Prove it United Kingdom

(a) Find all whole numbers $x$ such that $(x^2 - 7x + 11)^{(x^2-4x+4)} = 1.$ (7 marks)

(b) Find all whole numbers $x$ such that $(x^2 - 7x + 11)^{(x^2-4x+4)} = -1.$ (3 marks)

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