MathDB

3

Part of 2017 Caucasus Mathematical Olympiad

Problems(2)

pretty number theory

Source: II Caucasus Mathematical Olympiad

3/20/2018
Find the least positive integer nn satisfying the following statement: for eash pair of positive integers aa and bb such that 3636 divides a+ba+b and nn divides abab it follows that 3636 divides both aa and bb.
number theory
copy of existing problem

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