IMO Shortlist 2014 problem N7


Kvaliteta:
  Avg: 0,0
Težina:
  Avg: 9,0
Dodao/la: arhiva
7. svibnja 2017.
LaTeX PDF

Let c \geq 1 be an integer. Define a sequence of positive integers by a_1 = c and a_{n+1} = a_n^3 - 4c \cdot a_n^2 + 5c^2 \cdot a_n + c for all n \geq 1. Prove that for each integer n \geq 2 there exists a prime number p dividing a_n but none of the numbers a_1, \ldots, a_{n-1}.

(Austria)

Izvor: https://www.imo-official.org/problems/IMO2014SL.pdf