prime factorization

[afif mansib ch]

for n integer and p prime show that the exponent of the highest power of p appearing in the prime factorization of n! where
\[n=a_{k}p^k+a_{k-1}p^{k-1}+...a_{0}\]
is:
\[\frac{n-(a_{k}+...+a_{0})}{p-1}\]

[afif mansib ch]

no1's solved yet?here's my one.
\[\left [ n/p \right ]+...\left [ n/p^k \right ]\]
\[=\frac{a_{1}(p-1)+...+a_{k}(p^k-1)}{p-1}\]
\[=\frac{n-(a_{1}+..+a_{k})}{p-1}\]
has any1 solved it in some other way????

[nafistiham]

afif mansib ch wrote,

\[\left [ n/p \right ]+...\left [ n/p^k \right ]

maybe it should have been like this
\[\left [ n/p \right ]+...\left [ n/p^k \right ]\]

[afif mansib ch]

i wrote the same thing bt don't know why it came in such a form.

[nafistiham]

actually, you missed two buttons.
i copied the line and added ' \] '

[afif mansib ch]

thanks for the correction via.