Wednesday, November 17, 2010
6th International Mathematical Olympiad 1964 Problems & Solutions
A1. (a) Find all natural numbers n for which 7 divides 2n - 1.(b) Prove that there is no natural number n for which 7 divides 2n + 1. A2. Suppose that a, b, c are the sides of a triangle. Prove that: a2(b + c - a) + b2(c + a - b) + c2(a + b - c) ≤ 3abc. A3. Triangle ABC has sides a, b, c. Tangents to the inscribed circle are constructed parallel to the
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