$2+$ [ Factorization ]

After the lesson, Oleg bet with Sasha, claiming that he knows a natural number $m$, such that the number $m / 3 + m^{2} / 2 + m^{3} / 6$ is not an integer. Is Oleg right? And if he is, what is this number?
$\frac{m}{3}+\frac{m^{2}}{2}+\frac{m^{3}}{6}=\frac{m^{3}+3 m^{2}+2 m}{6}=\frac{m(m+1)(m+2)}{6}$. The product of three consecutive numbers is divisible by 6 (see problem 읻ㄱ). Therefore, the entire fraction is an integer for all natural $m$.

## Answer

Oleg is wrong.