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x^2 -\pi x+a < 0, 1998 integer solutions (IV Soros Olympiad 1997-98 R2 11.2)

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June 1, 2024
number theoryalgebrainequalities

Problem Statement

Find all values of the parameter aa for which there are exactly 19981998 integers xx satisfying the inequality x2−πx+a<0.x^2 -\pi x +a < 0.
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