How Many Integer Solutions Exist for a Sum Equation?

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Discussion Overview

The discussion revolves around finding the number of integer solutions for the equation n1 + n2 + n3 + n4 + ... + nk = p, focusing on the context of combinatorial mathematics and integer solutions.

Discussion Character

  • Exploratory, Technical explanation, Homework-related

Main Points Raised

  • Chaos initiates the discussion by asking for the formula to determine the number of integer solutions for the equation.
  • Another participant requests clarification on which variables are to be solved for and which are given.
  • A third participant references a Wikipedia page on the "Stars and Bars" theorem, suggesting it may contain relevant information.
  • Mathman confirms that the focus is on non-negative integer solutions for the variables, with p being a constant integer.

Areas of Agreement / Disagreement

Participants have not reached a consensus on the specific formula or method to be used, and the discussion includes multiple perspectives on how to approach the problem.

Contextual Notes

The discussion does not specify any assumptions about the values of n or p, nor does it clarify the conditions under which the solutions are to be found.

chaoseverlasting
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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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