2023 CMO(CHINA) Problems/Problem 1
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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 |