4th Swedish Mathematical Society Problems 1964

1.  Find the side lengths of the triangle ABC with area S and ∠BAC = x such that the side BC is as short as possible. 2.  Find all positive integers m, n such that n + (n+1) + (n+2) + ... + (n+m) = 1000. 3.  Find a polynomial with integer coefficients which has √2 + √3 and √2 + 31/3 as roots. 4.  Points H1, H2, ... , Hn are arranged in the