MathDB

3

Part of 2002 Polish MO Finals

Problems(2)

3 numbers written on blackboard

Source:

12/9/2005
Three non-negative integers are written on a blackboard. A move is to replace two of the integers k,mk,m by k+mk+m and ∣k−m∣|k-m|. Determine whether we can always end with triplet which has at least two zeros
combinatorics proposedcombinatorics
sequence and coprime elements

Source:

12/9/2005
kk is a positive integer. The sequence a1,a2,a3,...a_1, a_2, a_3, ... is defined by a1=k+1a_1 = k+1, an+1=an2−kan+ka_{n+1} = a_n ^2 - ka_n + k. Show that ama_m and ana_n are coprime (for m≠nm \not = n).
inductionnumber theory proposednumber theorystrong induction