Congruence statements, with a statement of percentage

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The discussion revolves around three congruence statements involving variables x, y, and z, each expressed as a percentage of their sum. The key question is whether these percentages uniquely determine the values of x, y, and z or at least restrict them to a specific subset of their respective congruence classes. Participants express uncertainty about applying the Chinese Remainder Theorem to this scenario, seeking clarification on its relevance. The conversation highlights the need for further elaboration on how the theorem can be integrated into solving the problem. Overall, the relationship between congruence percentages and their implications remains a focal point of inquiry.
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Suppose I have three statements of congruence:

x = a mod n, y = b mod m, z = c mod p;

Furthermore, x is a given percent of x + y + z, as is y and z.

Does this uniquely determine x, y, z? Or does it at least restrict x to a predictable subset of the congruence class of a, and so on?

Thank you.
 
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