MathDB

1

Part of 2017 Bulgaria EGMO TST

Problems(2)

A triangulation too acute to be cute

Source: Bulgaria EGMO TST 2017 Day 1 Problem 1

2/3/2023
Prove that every convex polygon has at most one triangulation consisting entirely of acute triangles.
combinatorial geometrytriangulationpolygoncombinatorics
Functional equation

Source: Turkish TST 2011 Problem 1

7/23/2011
Let Q+\mathbb{Q^+} denote the set of positive rational numbers. Determine all functions f:Q+→Q+f: \mathbb{Q^+} \to \mathbb{Q^+} that satisfy the conditions
f(xx+1)=f(x)x+1andf(1x)=f(x)x3 f \left( \frac{x}{x+1}\right) = \frac{f(x)}{x+1} \qquad \text{and} \qquad f \left(\frac{1}{x}\right)=\frac{f(x)}{x^3}
for all x∈Q+.x \in \mathbb{Q^+}.
functionalgorithminductionnumber theoryEuclidean algorithmalgebrafunctional equation