MathDB

6

Part of 1978 Romania Team Selection Test

Problems(2)

projection of polyhedrons

Source: Romanian TST 1978, Day 1, P6

9/28/2018
Show that there is no polyhedron whose projection on the plane is a nondegenerate triangle.
geometry3D geometryromania
infimum = 0

Source: Romanian TST 1978, Day 3, P6

9/30/2018
a) Prove that 0=inf⁡{∣x2+y3+y5∣∣x,y,z∈Z,x2+y2+z2>0} 0=\inf\{ |x\sqrt 2+y\sqrt 3+y\sqrt 5|\big| x,y,z\in\mathbb{Z} ,x^2+y^2+z^2>0 \}
b) Prove that there exist three positive rational numbers a,b,c a,b,c such that the expression E(x,y,z):=xa+yb+zc E(x,y,z):=xa+yb+zc vanishes for infinitely many integer triples (x,y,z), (x,y,z), but it doesn´t get arbitrarily close to 0. 0.
algebra