MathDB

2

Part of 1996 Turkey Team Selection Test

Problems(2)

Turkey TST 1996 Problem 2, P,E,F collinear

Source: Turkey TST 1996 Problem 2

9/28/2011
In a parallelogram ABCDABCD with ∠A<90\angle A < 90, the circle with diameter ACAC intersects the lines CBCB and CDCD again at EE and FF , and the tangent to this circle at AA meets the line BDBD at PP . Prove that the points PP, EE, FF are collinear.
geometryparallelogramtrigonometrygeometry proposed
Turkey TST 1996 Problem 5, n^2+an+b

Source: Turkey TST 1996 Problem 5

9/28/2011
Find the maximum number of pairwise disjoint sets of the form Sa,b={n2+an+b∣n∈Z}S_{a,b} = \{n^{2}+an+b | n \in \mathbb{Z}\}, a,b∈Za, b \in \mathbb{Z}.
linear algebramatrixnumber theory proposednumber theory