MathDB

2

Part of 2011 Akdeniz University MO

Problems(2)

number theory

Source:

1/31/2016
Let aa and bb is roots of the x2−6x+1x^2-6x+1 equation.
a) Show that, for all n∈Z+n \in{\mathbb Z^+} , an+bna^n+b^n is a integer. b) Show that, for all n∈Z+n \in{\mathbb Z^+} , 55 isn't divide an+bna^n+b^n
number theorynumber theory unsolved
question

Source:

1/29/2016
Let OO is a point in a plane PP and let [OX,[OY,[OZ[OX,[OY,[OZ is distinct ray in PP. Prove that, if A∈[OXA \in [OX , B∈[OYB \in [OY and C∈[OZC \in [OZ points such that △OAB\triangle OAB , △OBC\triangle OBC and △OCA\triangle OCA 's perimeter is 2, there is only one (A,B,C)(A,B,C) triple
Plane Geometrygeometry