MathDB

1

Part of 1992 Turkey Team Selection Test

Problems(2)

Turkey TST 1992 - P1: 14 conseq. divisible by first 5 primes

Source:

3/13/2011
Is there 1414 consecutive positive integers such that each of these numbers is divisible by one of the prime numbers pp where 2≤p≤112\leq p \leq 11.
number theoryprime numbersnumber theory proposed
Turkey TST 1992 - P4: PQ+RS=QR+SP in cyclic quadrilateral

Source:

3/13/2011
The feet of perpendiculars from the intersection point of the diagonals of cyclic quadrilateral ABCDABCD to the sides AB,BC,CD,DAAB,BC,CD,DA are P,Q,R,SP,Q,R,S, respectively. Prove PQ+RS=QR+SPPQ+RS=QR+SP.
geometrycyclic quadrilateralgeometry proposed