finding the number of solutions of an equation over $mathbb{Z}_{ge 0}$
I want to count the number of solutions to the following equation in non-negative integers:
Let $n in mathbb{N}$,
Fix $1 le p le q le n$ and $m_p, m_q in mathbb{N}$,
$$sum_{j = 1}^n j cdot x_j = n $$.
Question : How many solutions $(x_j)_{1 le j le n}$ are there for the above equation such that
1) $x_j$'s are non negative integers
2) $x_p ge m_p$ and $x_q ge m_q$.
Kindly share your views.
Thank you.
linear-diophantine-equations
asked Dec 26 '18 at 18:00
GA316
2,6431132
add a comment |
I want to count the number of solutions to the following equation in non-negative integers:
Let $n in mathbb{N}$,
Fix $1 le p le q le n$ and $m_p, m_q in mathbb{N}$,
$$sum_{j = 1}^n j cdot x_j = n $$.
Question : How many solutions $(x_j)_{1 le j le n}$ are there for the above equation such that
1) $x_j$'s are non negative integers
2) $x_p ge m_p$ and $x_q ge m_q$.
Kindly share your views.
Thank you.
linear-diophantine-equations
asked Dec 26 '18 at 18:00
GA316
2,6431132
add a comment |
I want to count the number of solutions to the following equation in non-negative integers:
Let $n in mathbb{N}$,
Fix $1 le p le q le n$ and $m_p, m_q in mathbb{N}$,
$$sum_{j = 1}^n j cdot x_j = n $$.
Question : How many solutions $(x_j)_{1 le j le n}$ are there for the above equation such that
1) $x_j$'s are non negative integers
2) $x_p ge m_p$ and $x_q ge m_q$.
Kindly share your views.
Thank you.
linear-diophantine-equations
asked Dec 26 '18 at 18:00
GA316
2,6431132
I want to count the number of solutions to the following equation in non-negative integers:
Let $n in mathbb{N}$,
Fix $1 le p le q le n$ and $m_p, m_q in mathbb{N}$,
$$sum_{j = 1}^n j cdot x_j = n $$.
Question : How many solutions $(x_j)_{1 le j le n}$ are there for the above equation such that
1) $x_j$'s are non negative integers
2) $x_p ge m_p$ and $x_q ge m_q$.
Kindly share your views.
Thank you.
linear-diophantine-equations
linear-diophantine-equations
asked Dec 26 '18 at 18:00
GA316
2,6431132
asked Dec 26 '18 at 18:00
GA316
2,6431132
edited Dec 27 '18 at 16:17
asked Dec 26 '18 at 18:00
GA316
2,6431132
asked Dec 26 '18 at 18:00
GA316
2,6431132
asked Dec 26 '18 at 18:00
GA316
2,6431132
2,6431132
add a comment |
add a comment |
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