3
Part of 2005 Irish Math Olympiad
Problems(2)
probably known
Source: Ireland 2005
7/6/2009
Prove that the sum of the lengths of the medians of a triangle is at least three quarters of its perimeter.
inequalitiestriangle inequalitygeometry unsolvedgeometry
divisibility
Source: Ireland 2005
7/6/2009
Let be an integer and be odd positive integers. Prove that divides x^{y^{z^w}}\minus{}x^{y^z}.
modular arithmeticnumber theory unsolvednumber theory