23 lines
652 B
Markdown
23 lines
652 B
Markdown
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Consider quadratic Diophantine equations of the form:
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~~~
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x^2 – Dy^2 = 1
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For example, when `D=13`, the minimal solution in `x` is `649^2 – 13×180^2 = 1`.
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It can be assumed that there are no solutions in positive integers when D is square.
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By finding minimal solutions in `x` for `D = {2, 3, 5, 6, 7}`, we obtain the following:
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3^2 – 2×2^2 = 1
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2^2 – 3×1^2 = 1
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9^2 – 5×4^2 = 1
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5^2 – 6×2^2 = 1
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8^2 – 7×3^2 = 1
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Hence, by considering minimal solutions in `x` for `D <= 7`, the largest `x` is obtained when `D=5`.
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Find the value of `D <= 1000` in minimal solutions of `x` for which the largest value of `x` is obtained.
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