36th Eötvös Competition Problems 1932

1.  Show that if m is a multiple of an, then (a + 1)m -1 is a multiple of an+1. 2.  ABC is a triangle with AB and AC unequal. AM, AX, AD are the median, angle bisector and altitude. Show that X always lies between D and M, and that if the triangle is acute-angled, then angle MAX < angle DAX.