MathDB

3

Part of 1993 Polish MO Finals

Problems(2)

Sequence and the greatest odd divisor

Source: Problem 3, Polish NO 1993

10/6/2005
Denote g(k)g(k) as the greatest odd divisor of kk. Put f(k)=k2+kg(k)f(k) = \dfrac{k}{2} + \dfrac{k}{g(k)} for kk even, and 2(k+1)/22^{(k+1)/2} for kk odd. Define the sequence x1,x2,x3,...x_1, x_2, x_3, ... by x1=1x_1 = 1, xn+1=f(xn)x_{n+1} = f(x_n). Find nn such that xn=800x_n = 800.
number theory solvednumber theory
Volume of tetrahedron

Source: Problem 6, Polish NO 1993

10/6/2005
Find out whether it is possible to determine the volume of a tetrahedron knowing the areas of its faces and its circumradius.
geometry3D geometrytetrahedroncircumcirclegeometry unsolved