2023 CMO Problems/Problem 1
Revision as of 04:37, 25 May 2024 by Anyu tsuruko (talk | contribs)
Problem
Find the smallest real number such that any positive integer
can be expressed as the product of 2023 positive integers
, where for each
, either
is a prime number or
.
Solution 1
1. Let . Then there exist
and
.
2. Assume
where
and
with
. Also, let
be primes and
We will show that .
Suppose otherwise, that
. Then
which leads to a contradiction.
Therefore, the minimum
is:
~moving|szm
See also
2023 CMO(CHINA) (Problems • Resources) | ||
Preceded by First Problem |
Followed by Problem 2 | |
1 • 2 • 3 • 4 • 5 • 6 | ||
All CMO(CHINA) Problems and Solutions |