Congruence statements, with a statement of percentage

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SUMMARY

The discussion centers on the application of the Chinese Remainder Theorem (CRT) in determining the values of x, y, and z given their congruence statements: x = a mod n, y = b mod m, and z = c mod p. The user queries whether specifying x as a percentage of the sum x + y + z uniquely determines these values or restricts x to a predictable subset of its congruence class. The consensus indicates that while the CRT provides a framework for solving such congruences, the additional percentage condition complicates the direct application of the theorem.

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1MileCrash
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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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