by fungarwai, Sep 13, 2019, 12:14 PM
Let
For p=2,
There are
different ways to choose
for
For p=3,
There are
different ways to choose
for
and
different ways to choose
for
Proof
Let
There are
different ways to choose
for
Consider the sum of coefficient of the odd power of generating function
There are
different ways to choose
for
and
different ways to choose
for
Multiplying the result
There are
different ways to choose
for
and
different ways to choose
for
For p=5,
The number of
is
The number of
is
The number of
is
The number of
is
Proof
Example
The number of
is
The number of
is
The number of
is
The number of
is
The number of
is
The number of
is
The number of
is
The number of
is
The number of
is
The number of
is
The number of
is
The number of
is
This post has been edited 1 time. Last edited by fungarwai, Sep 13, 2019, 12:15 PM