Inspired by Nihar Mahajan's featured problem
Number Theory
Level
3
In each of the cases below, there exists only one solution whereby the sum of \(n\) positive integers equals the product.
- For \(n=2\), we have \(2+2=2\times 2\).
- For \(n=3\), we have \(1+2+3=1\times2\times3\).
- For \(n=4\), we have \(1+1+2+4=1\times 1\times2\times4\).
If solution(s) exist for \(n=5,\) find the sum of all possible sums (or equivalently, products).
If such a solution does not exist, submit your answer as 0.
by
Noel Lo