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11.1

Part of IV Soros Olympiad 1997 - 98 (Russia)

Problems(3)

diophantine xy =1997(x + y) (IV Soros Olympiad 1997-98 Correspondence 11.1)

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6/1/2024
Solve the equation xy=1997(x+y)xy =1997(x + y) in integers.
number theoryDiophantine equationdiophantine
dig together the garden bed (IV Soros Olympiad 1997-98 R2 11.1)

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6/1/2024
Petya digs the garden bed alone for aa minutes longer than he does with Vasya. Vasya digs up the same bed for bb minutes longer than he would have done with Petya. How many minutes does it take Vasya and Petya to dig up the same bed together? orthogonal).
algebra
2 arc cos x >= arc cos y (IV Soros Olympiad 1997-98 R3 11.1)

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6/2/2024
On the coordinate plane, draw a set of points whose coordinates (x,y)(x, y) satisfy the inequality 2arccos⁡x≥arccos⁡y2 arc \cos x \ge arc \cos y
analytic geometrytrigonometry