How do we find the number of non-negative integer solutions for linear equation of the form: a

Warren Leach

Warren Leach

Answered question

2022-06-04

How do we find the number of non-negative integer solutions for linear equation of the form:
a x + b y = c
Where a , b , c are constants and x , y are the variables ?

Answer & Explanation

Shayna Woods

Shayna Woods

Beginner2022-06-05Added 3 answers

Not a complete answer, but a relatively simple one and approximate one. By Schur's theorem of combinatorics?, the number of solutions is asymptotically c :
c a b
Schur's theorem of combinatorics states that the number of solutions of (with a i relatively prime):
i = 1 M a i x i = c
is:
c M 1 ( M 1 ) ! a i
This name is used by Wilf's Generatingfunctionology, but I cannot seem to find it elsewhere. It appears that Schur has many theorems.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?