2
Part of 2012 IberoAmerican
Problems(2)
Ibero American 2012 - Problem 2
Source: Ibero American 2012
10/2/2012
A positive integer is called shiny if it can be written as the sum of two not necessarily distinct integers and which have the same sum of their digits. For instance, is shiny, because , and both and have the same sum of their digits. Find all positive integers which are not shiny (the dark integers).
number theory proposednumber theory
Ibero American 2012 - Problem 5
Source:
10/3/2012
Let be a triangle, and the intersections of the parallel line to that passes through with the external angle bisectors of angles and , respectively. The perpendicular to at and the perpendicular to at meet at . Let be the incenter of . Show that .
geometryincentersymmetrygeometric transformationhomothetyparallelogramangle bisector