13th Swedish Mathematical Society Problems 1973

1.  log82 = 0.2525 in base 8 (to 4 places of decimals). Find log84 in base 8 (to 4 places of decimals). 2.  The Fibonacci sequence f1, f2, f3, ... is defined by f1 = f2 = 1, fn+2 = fn+1 + fn. Find all n such that fn = n2. 3.  ABC is a triangle with ∠A = 90o, ∠B = 60o. The points A1, B1, C1 on BC, CA, AB respectively are such that