2008 UNCO Math Contest II Problems/Problem 5

Revision as of 02:02, 13 January 2019 by Timneh (talk | contribs) (Solution)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem

5. The sum of $400, 3, 500, 800$ and $305$ is $2008$ and the product of these five numbers is $146400000000 = 1464 \times 10^8.$

(a) Determine the largest number which is the product of positive integers whose sum is $2008$.

(b) Determine the largest number which is the product of positive integers whose sum is $n$.


Solution

(a) $3^{668}\cdot 2^2$ (b) $3^k$ if $n=3k$; $2^2\cdot 3^{k-1}$ if $n=3k+1$; $2\cdot 3^{k}$ if $n=3k+2$

See Also

2008 UNCO Math Contest II (ProblemsAnswer KeyResources)
Preceded by
Problem 4
Followed by
Problem 6
1 2 3 4 5 6 7 8 9 10
All UNCO Math Contest Problems and Solutions
Invalid username
Login to AoPS