MathDB

2

Part of 2009 Bosnia Herzegovina Team Selection Test

Problems(2)

Bosnia 2009 Problem 2 a^2(b-a)/(b+a) = square of prime

Source:

8/12/2010
Find all pairs (a,b)\left(a,b\right) of posive integers such that a2(b−a)b+a\frac{a^{2}\left(b-a\right)}{b+a} is square of prime.
number theory proposednumber theory
Bosnia 2009 Problem 5

Source:

8/8/2010
Line pp intersects sides ABAB and BCBC of triangle △ABC\triangle ABC at points MM and K.K. If area of triangle △MBK\triangle MBK is equal to area of quadrilateral AMKC,AMKC, prove that ∣MB∣+∣BK∣∣AM∣+∣CA∣+∣KC∣≥13\frac{\left|MB\right|+\left|BK\right|}{\left|AM\right|+\left|CA\right|+\left|KC\right|}\geq\frac{1}{3}
geometrygeometry proposed