How Many Integer Solutions Exist for a Sum Equation?

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The discussion centers around finding the number of integer solutions for the equation n1 + n2 + n3 + n4 + ... + nk = p, specifically for non-negative integers. A participant requests clarification on which variables are fixed and which are to be solved. The "stars and bars" combinatorial method is suggested as a solution approach. The focus is on determining integer solutions where the sum equals a constant integer p. This method is essential for solving similar combinatorial problems in mathematics.
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It's been a while since I've done equation based math (I'm doing an MBA now) and there's a formula that I can't for the life of me remember.


If you have a set of number such as

n1 + n2+ n3+ n4... +nk =p,

How many integer solutions does this equation have?

TIA,

Chaos
 
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chaoseverlasting said:
It's been a while since I've done equation based math (I'm doing an MBA now) and there's a formula that I can't for the life of me remember.


If you have a set of number such as

n1 + n2+ n3+ n4... +nk =p,

How many integer solutions does this equation have?

TIA,

Chaos
Could you clarify - which of the items are to be solved for and which are given?
 
Thank you awkward, that's exactly what I was looking for! Mathman, its the integer solution for non negative integer values of n1, n2, n3, n4 and where p is constant integer.
 

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