9th Swedish Mathematical Society Problems 1969

1.  Find all integers m, n such that m3 = n3 + n. 2.  Show that tan π/3n is irrational for all positive integers n. 3.  a1 ≥ a2 ≥ ... ≥ an is a sequence of reals. b1, b2, b3, ... bn is any rearrangement of the sequence B1 ≥ B2 ≥ ... ≥ Bn. Show that ∑ aibi ≤ &sum aiBi. 4.  Define g(x) as the largest value of |y2 - xy| for