MathDB

3

Part of 2008 Czech and Slovak Olympiad III A

Problems(2)

czech republic,czech and slovakia MO(third round),2008 p3

Source:

2/25/2012
Find all pairs of integers (a,b)(a,b) such that a2+ab+1∣b2+ab+a+b−1a^2+ab+1\mid b^2+ab+a+b-1.
number theorygreatest common divisornumber theory proposed
czech republic,czech and slovakia MO(third round),2008 p6

Source:

2/25/2012
Find the greatest value of pp and the smallest value of qq such that for any triangle in the plane, the inequality p<a+mb+n<qp<\frac{a+m}{b+n}<q holds, where a,ba,b are it's two sides and m,nm,n their corresponding medians.
inequalitiesinequalities proposedgeometric inequalityTrianglemedian