MathDB

2

Part of 2006 Junior Balkan Team Selection Tests - Moldova

Problems(2)

Poblem 2 (jbmo tst), moldova

Source: JBMO TST, Moldova

3/31/2006
Prove that there infinitely many numbers of the form 18m+45m+50m+125m18^{m}+45^{m}+50^{m}+125^{m}, divisible by 2006. m∈Nm\in N
number theory proposednumber theory
Problem 2 (2nd jbmo tst)

Source: 2nd TST for JBMO, Moldova

3/31/2006
Let ABCDABCD be a rectangle and denote by MM and NN the midpoints of ADAD and BCBC respectively. The point PP is on (CD(CD such that D∈(CP)D\in (CP), and PMPM intersects ACAC in QQ. Prove that m(∠MNQ)=m(∠MNP)m(\angle{MNQ})=m(\angle{MNP}).
geometryrectangleprojective geometryangle bisectorgeometry proposed