MathDB

5

Part of 2008 Saint Petersburg Mathematical Olympiad

Problems(2)

St Petersburgh 2008 #5

Source:

7/23/2011
Given are distinct natural numbers aa, bb, and cc. Prove that gcd⁡(ab+1,ac+1,bc+1)≤a+b+c3 \gcd(ab+1, ac+1, bc+1)\le \frac{a+b+c}{3}
modular arithmeticquadraticsnumber theory proposednumber theory
Tetrahedron

Source: St Petersburg Olympiad 2008, Grade 11, P5

8/30/2017
All faces of the tetrahedron ABCDABCD are acute-angled triangles.AKAK and ALAL -are altitudes in faces ABCABC and ABDABD. Points C,D,K,LC,D,K,L lies on circle. Prove, that AB⊥CDAB \perp CD
geometry3D geometrytetrahedron