MathDB

2

Part of 2006 Bundeswettbewerb Mathematik

Problems(2)

x³+y³=4·(x²y+xy²+1)

Source: Germany Bundeswettbewerb Mathematik 2006, Day 1, Problem 2

4/4/2006
Prove that there are no integers x,yx,y for that it is x3+y3=4⋅(x2y+xy2+1)x^3+y^3=4\cdot(x^2y+xy^2+1).
calculusintegrationgeometry3D geometry
functional eq from positive rationals

Source:

3/5/2007
Find all functions f:Q+→Rf: Q^{+}\rightarrow R such that f(x)+f(y)+2xyf(xy)=f(xy)f(x+y)f(x)+f(y)+2xyf(xy)=\frac{f(xy)}{f(x+y)} for all x,y∈Q+x,y\in Q^{+}
functioninductionalgebra unsolvedalgebra