Determine the Nonnegative Integers
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Please see the attachment for problem related to nonnegative integer and my solution (needs to be edited and confirmed).
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Solution Summary
The solution determines the nonnegative integers in the problem.
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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.")
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