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If a ≡ b mod(n) and b ≡ c mod(n) , then

If a ≡ b mod(n) and b ≡ c mod(n) , then Correct Answer a ≡ c mod(n)

Concept:

For any integers a and b, and positive integer n, we have:

  •  If a ≡ b mod n then b ≡ a mod n.
  •  If a ≡ b mod n and b  ≡ c mod n then a ≡ c mod n

 

Explanation:

As discussed above, we know that

If a ≡ b mod n and b  ≡ c mod n then a ≡ c mod n

Then,

a ≡ c mod(n)

Important Points1.  If a ≡ b mod n then b = a + nq for some integer q, and conversely.

2. If a ≡ b mod n then a and b leave the same remainder when divided by n. 

3. If gcd(a, n) = 1, then the congruence ax ≡ b mod n has a solution x = c. In this case, the general solution of the congruence is given by x ≡ c mod n.

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