Maths Olympiad Prep

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, 2024

Algebra Difficulty 5.0 AIME, harder Prove it United Kingdom

(a) The equation uv+3u3v18=0uv + 3u - 3v - 18 = 0 is equivalent to (ua)(v+b)=9(u-a)(v+b) = 9. Write down the values of aa and bb. (1 mark) (b) Hence find all integer solutions of the equation uv+3u3v18=0uv + 3u - 3v - 18 = 0. (3 marks) (Note: 'integers' means whole numbers, which can be positive, negative or zero.) (c) Find all integer solutions of the equation x2y2+6y18=0x^2 - y^2 + 6y - 18 = 0. (6 marks)

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