Understanding Congruency and Its Applications

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Congruency in mathematics indicates that two numbers give the same remainder when divided by a specific modulus. For example, 333 is congruent to 3 mod 10, meaning both numbers leave a remainder of 3 when divided by 10. This allows for the replacement of 333 with 3 in calculations involving mod 10, simplifying the process. The discussion clarifies that the technical definition can be understood more simply as equivalence in terms of remainders. Overall, the concept of congruency streamlines mathematical operations by allowing the use of smaller, equivalent numbers.
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I'm having a bit of trouble understanding what it means for one number to be congruent to another. I have this more technical definition but I was wondering if anyone could put it into more simple terms.

What I really want to know is that if say 333 is congruent to 3 mod 10, does that mean that 333 is equivalent to 3 mod 10? Can I replace 333 by just 3?

I am looking a lot of examples in my notes and I see numbers being replaced by their congruencies, is that allowed?
 
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Nope,it means that both 333 and 3 give the same remainder when divided by 10,naely 3.

Daniel.
 
That's all? : Nothing more? Well that makes things more simple then. I was thinking there was more to it. Thanks.
 

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