Given an expression, a ≡ b (mod n), read as a is congruent to b modulo n, which of the following expressions is correct? (Wentz QOTD)
A. 7 ≡ 1 (mod 4)
B. 7 ≡ 2 (mod 5)
C. 7 ≡ 3 (mod 6)
D. 7 ≡ 4 (mod 7)

Kindly be reminded that the suggested answer is for your reference only. It doesn’t matter whether you have the right or wrong answer. What really matters is your reasoning process and justifications.

My suggested answer is B. 7 ≡ 2 (mod 5).

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The expression, a ≡ b (mod n), means “a and b have the same remainder when they are divided by n.” That is, (a mod n) equals (b mod n).

• 7 ≡ 1 (mod 4) => (7 mod 4) = 3, (1 mod 4) = 1 but 3 <> 1
• 7 ≡ 2 (mod 5) => (7 mod 5) = 2, (2 mod 5) = 2 and 2 == 2
• 7 ≡ 3 (mod 6) => (7 mod 6) = 1, (3 mod 6) = 3 but 1 <> 3
• 7 ≡ 4 (mod 7) => (7 mod 7) = 0, (4 mod 7) = 4 but 0 <> 4

Reference

• Modular arithmetic
• Multiplicative order
• Modulo operation
• RSA problem
• RSA (cryptosystem)
• RSA Algorithm in Cryptography

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給定一個表達式，a ≡ b (mod n)，讀作 a 與 b 關於模 n 同餘，以下哪個表達式是正確的？ (Wentz QOTD)
A. 7 ≡ 1 (mod 4)
B. 7 ≡ 2 (mod 5)
C. 7 ≡ 3 (mod 6)
D. 7 ≡ 4 (mod 7)