# Determine the Nonnegative Integers

Please see the attachment for problem related to nonnegative integer and my solution (needs to be edited and confirmed).

Â© BrainMass Inc. brainmass.com November 24, 2022, 11:53 am ad1c9bdddfhttps://brainmass.com/math/basic-algebra/determine-nonnegative-integers-27790

#### Solution Preview

Please see attached file

The answer is correct, and clear, so I only made some changes (in bold) which I think may make more sense.

Estimated Time/Compensation: 30 min/$8

Date Needed/Deadline: Sunday, November 7, 2004. 1:00 P.M. Pacific

There is a solution that is already provided.

I ask that you check the solution correctness, and clarity.

If there is a proof, please do your best to explain the proof clearer, with words.

If you find an error , mistake, or something could be "more elegant" than please rework the entire solution.

PLEASE FOLLOW THE INSTRUCTIONS:

1. No programming

2. Show all steps

3. Explain your solution process in words

4. Proofs need to be explained primarily in words. If there is a lot of algebra, explain the process in words as well.

5. ANSWER ALL PARTS OF THE QUESTION

For every nonnegative integer n, there are unique nonnegative integers i and j such that

and

To see this, consider division of n by 43, and let i and j denote the quotient and the remainder, respectively:

j is an element of Z43, and n is said to be congruent modulo 43 to j, which we could express by saying that n is EQUIVALENT to j (modulo 43). (In YOUR notation, we would say that "n = j in Z43.")

------------------------------------------------------------------

If ...

#### Solution Summary

The solution determines the nonnegative integers in the problem.