MathDB

1

Part of 1989 China Team Selection Test

Problems(2)

maximum value of the coincident triangle area

Source: China TST 1989, problem 1

6/27/2005
A triangle of sides 32,52,2\frac{3}{2}, \frac{\sqrt{5}}{2}, \sqrt{2} is folded along a variable line perpendicular to the side of 32.\frac{3}{2}. Find the maximum value of the coincident area.
geometrygeometry unsolved
Does there exist a function f^{1989}(n) = 2n

Source: China TST 1989, problem 5

6/27/2005
Let N={1,2,…}.\mathbb{N} = \{1,2, \ldots\}. Does there exists a function f:N↦Nf: \mathbb{N} \mapsto \mathbb{N} such that ∀n∈N,\forall n \in \mathbb{N}, f1989(n)=2⋅nf^{1989}(n) = 2 \cdot n ?
functionalgebra unsolvedalgebra