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,