12th All Soviet Union Mathematical Olympiad Problems 1978

1.  an is the nearest integer to √n. Find 1/a1 + 1/a2 + ... + 1/a1980. 2.  ABCD is a quadrilateral. M is a point inside it such that ABMD is a parallelogram. ∠CBM = ∠CDM. Show that ∠ACD = ∠BCM. 3.  Show that there is no