MathDB

4

Part of 2017 Caucasus Mathematical Olympiad

Problems(2)

II Caucasus Mathematical Olympiad, 9.4

Source: II Caucasus Mathematical Olympiad

3/20/2018
In an acute traingle ABCABC with AB<BCAB< BC let BHbBH_b be its altitude, and let OO be the circumcenter. A line through HbH_b parallel to COCO meets BOBO at XX. Prove that XX and the midpoints of ABAB and ACAC are collinear.
geometry
number theory construction

Source: II Caucasus Mathematical Olympiad

3/20/2018
Determine if there exist 101101 positive integers (not necessarily distinct) such that their product is equal to the sum of all their pairwise LCM.
number theory