Neka je
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
prirodan broj kojem je zapis u decimalnom sustavu dan sa
![\overline{a_ma_{m-1}...a_1}](/media/m/3/6/c/36c66ac713bab6696e75314c62cce7c9.png)
. Gdje je svaki
![a_i](/media/m/2/a/2/2a22407e8a19d2df9d425caa379f34a8.png)
,
![i \in \{1,2,...,m\}](/media/m/b/3/4/b341f5c5e961d59ff89034563dbcf0aa.png)
prirodan broj.
Odredi najveći
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
za koji vrijedi:
![n=\prod_{i=1}^{m}(a_i + 1)](/media/m/d/b/d/dbd2b798245acf9a1e6fd83a22f88b49.png)
.
Let
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
be positive integer with the decimal representation
![\overline{a_ma_{m-1}...a_1}](/media/m/3/6/c/36c66ac713bab6696e75314c62cce7c9.png)
. where every
![a_i](/media/m/2/a/2/2a22407e8a19d2df9d425caa379f34a8.png)
,
![i \in \{1,2,...,m\}](/media/m/b/3/4/b341f5c5e961d59ff89034563dbcf0aa.png)
is a positive integer.
What is the maximum
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
for which the following holds:
![n=\prod_{i=1}^{m}(a_i + 1)](/media/m/d/b/d/dbd2b798245acf9a1e6fd83a22f88b49.png)
.
[lang=hr]
Neka je $n$ prirodan broj kojem je zapis u decimalnom sustavu dan sa $\overline{a_ma_{m-1}...a_1}$. Gdje je svaki $a_i$, $i \in \{1,2,...,m\}$ prirodan broj.
\\Odredi najveći $n$ za koji vrijedi: $$n=\prod_{i=1}^{m}(a_i + 1)$$.
[/lang]
[lang=en]
Let $n$ be positive integer with the decimal representation $\overline{a_ma_{m-1}...a_1}$. where every $a_i$, $i \in \{1,2,...,m\}$ is a positive integer.
\\What is the maximum $n$ for which the following holds: $$n=\prod_{i=1}^{m}(a_i + 1)$$.
[/lang]