Tuesday, October 26, 2010
15th Swedish Mathematical Society Problems 1975
1. A is the point (1, 0), L is the line y = kx (where k > 0). For which points P (t, 0) can we find a point Q on L such that AQ and QP are perpendicular?2. Is there a positive integer n such that the fractional part of (3 + √5)n > 0.99? 3. Show that an + bn + cn ≥ abn-1 + bcn-1 + can-1 for real a, b, c ≥ 0 and n a positive integer. 4. P1,
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