Prove that a equiv b mod n if and only if na

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Prove that a equiv b mod n if and only if na - b that is

1. Let ∼ be defined so that a ∼ b exactly when a · b is divisible by 3. Is this an equivalence relation? If not, which of the three properties (reflexive, symmetric, transitive) does not hold?

2. Encrypt the message we are all made of stars using the atbash cipher.

3. Prove that a ≡ b (mod n) if and only if n|(a - b); that is, check that the condition given in Definition 5.3.1 is correct.

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Mathematics: Prove that a equiv b mod n if and only if na - b that is

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Mathematics: Prove that a equiv b mod n if and only if na - b that is

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