MathDB

1

Part of 2003 Irish Math Olympiad

Problems(2)

Easy number theory

Source: Irish Math Olympiad 2003

5/1/2017
find all solutions, not necessarily positive integers for (m2+n)(m+n2)=(m+n)3(m^2+ n)(m+ n^2)= (m+ n)^3
Diophantine equationnumber theory
Algebraic ineq in triangle

Source:

1/5/2006
If a,b,ca,b,c are the sides of a triangle whose perimeter is equal to 2 then prove that: a) abc+2827≥ab+bc+acabc+\frac{28}{27}\geq ab+bc+ac; b) abc+1<ab+bc+acabc+1<ab+bc+ac See also http://www.mathlinks.ro/Forum/viewtopic.php?t=47939&view=next (problem 1) :)
geometryperimeterinequalitiestriangle inequality