Final answer:
Two integers are congruent modulo n if they have the same remainder when divided by n. This relationship is expressed as a ≡ b (mod n) and is fundamental in modular arithmetic, allowing addition and subtraction within the modular system.
Step-by-step explanation:
Two integers a and b are said to be congruent modulo n if (a mod n) = (b mod n). This means that when a and b are divided by n, they leave the same remainder. Thus, a ≡ b (mod n) can also be written as n | (a - b), which means n is a divisor of the difference between a and b.
When dealing with congruences, you operate within a system that revolves around a fixed modulus n. Just like addition and subtraction, congruence relations can be manipulated. For example, if c is another integer and a ≡ b (mod n), then it follows that (a + c) ≡ (b + c) (mod n) and (a - c) ≡ (b - c) (mod n).