MathDB

2

Part of 2017 239 Open Mathematical Olympiad

Problems(2)

n=xy implies x+y is a power of 2

Source: 239 2017 J3 S2

5/22/2020
Find all composite numbers nn such that for each decomposition of n=xyn=xy, x+yx+y be a power of 22.
number theory
prove that circles pass through a fixed point

Source: 239 2017 J2

5/31/2020
Inside the circle ω\omega through points A,BA, B point CC is chosen. An arbitrary point XX is selected on the segment BCBC. The ray AXAX cuts the circle in YY. Prove that all circles CXYCXY pass through a two fixed points that is they intersect and are coaxial, independent of the position of XX.
geometrycoaxial circlesInversion