MathDB

2

Part of 2000 IMC

Problems(2)

find all pairs

Source: IMC 2000 day 1 problem 2

10/29/2005
Let p(x)=x5+xp(x)=x^5+x and q(x)=x5+x2q(x)=x^5+x^2, Find al pairs (w,z)∈C×C(w,z)\in \mathbb{C}\times\mathbb{C}, w≠zw\not=z for which p(w)=p(z),q(w)=q(z)p(w)=p(z),q(w)=q(z).
complex analysiscomplex analysis unsolved
continuous but nowhere monotone function

Source: IMC 2000 day 2 problem 2

10/29/2005
Let ff be continuous and nowhere monotone on [0,1][0,1]. Show that the set of points on which ff obtains a local minimum is dense.
functionreal analysisreal analysis unsolved