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We have this equation : $$x_1 + x_2 + x_3 + \dots + x_n = c $$

How we can find number of non repetitive solutions in natural numbers or integer numbers ?

S.H.W
  • 4,379
  • This is an application of the stars and bars argument. In this case, it is ${c+n-1} \choose {c}$ – AndroidFish Dec 02 '16 at 17:14
  • Can you show the proof of this expression ? – S.H.W Dec 02 '16 at 17:19
  • http://math.stackexchange.com/questions/910809/how-to-use-stars-and-bars-combinatorics shows how to use the bars and stars idea, and https://en.wikipedia.org/wiki/Stars_and_bars_%28combinatorics%29 has proofs and more general information.

    I won't reprove them as there is a lot of information, proofs, and examples using it and solving generalized diophantine equations, but these links will help you understand the method.

     – AndroidFish Dec 02 '16 at 17:37
  • @AndroidFish How we can use this formula for this question : http://math.stackexchange.com/questions/2040444/count-the-number-of-possible-solutions – S.H.W Dec 02 '16 at 18:13

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