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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