MEMO 2017 ekipno problem 8


Kvaliteta:
  Avg: 0,0
Težina:
  Avg: 6,0
Dodao/la: arhiva
12. rujna 2018.
LaTeX PDF

For an integer n \geqslant 3 we define the sequence \alpha_1, \alpha_2, \ldots, \alpha_k as the sequence of exponents in the prime factorization of n! = p_1^{\alpha_1}p_2^{\alpha_2} \ldots p_k^{\alpha_k}, where p_1 < p_2 < \ldots < p_k are primes. Determine all integers n \geq 3 for which \alpha_1, \alpha_2, \ldots, \alpha_k is a geometric progression.

Izvor: Srednjoeuropska matematička olimpijada 2017, ekipno natjecanje, problem 8