IMO Shortlist 1977 problem 10


Kvaliteta:
  Avg: 0.0
Težina:
  Avg: 0.0
Dodao/la: arhiva
April 2, 2012
LaTeX PDF
Let n be a given number greater than 2. We consider the set V_n of all the integers of the form 1 + kn with k = 1, 2, \ldots A number m from V_n is called indecomposable in V_n if there are not two numbers p and q from V_n so that m = pq. Prove that there exist a number r \in V_n that can be expressed as the product of elements indecomposable in V_n in more than one way. (Expressions which differ only in order of the elements of V_n will be considered the same.)
Source: Međunarodna matematička olimpijada, shortlist 1977