MathDB

1

Part of 1996 Polish MO Finals

Problems(2)

2x^2+2x+1 divides (x+1)^n - r

Source:

10/30/2005
Find all pairs (n,r)(n,r) with nn a positive integer and rr a real such that 2x2+2x+12x^2+2x+1 divides (x+1)n−r(x+1)^n - r.
trigonometrynumber theory unsolvednumber theory
Tetrahedron and equality of segments

Source:

10/30/2005
ABCDABCD is a tetrahedron with ∠BAC=∠ACD\angle BAC = \angle ACD and ∠ABD=∠BDC\angle ABD = \angle BDC. Show that AB=CDAB = CD.
geometry3D geometrytetrahedrongeometry unsolved