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## Homework Statement

I am trying to learn the Chinese Remainder Theorem from the following website:

http://www.libraryofmath.com/chinese-remainder-theorem.html

The only thing I dont understand is why the end result is expressed as another linear congruence. In the first example, the solution is expressed as 53(mod 84). But x = 53 solves all the equations. Similarly, in the third example, they give the solution as 263 is congruent to 233(mod105) yet x = 263 solves the system. If on tomorrows final I only gave the numbers x = 53 or x = 263 as solutions to systems of congruences, would that be wrong? Thanks and sorry for redirecting you to a different site.