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In a modular arithmetic system, if a ≡ b (mod m), which of the following stateme

Practice Questions

Q1
In a modular arithmetic system, if a ≡ b (mod m), which of the following statements is true?
  1. a - b is divisible by m
  2. a + b is divisible by m
  3. a * b is divisible by m
  4. a / b is divisible by m

Questions & Step-by-Step Solutions

In a modular arithmetic system, if a ≡ b (mod m), which of the following statements is true?
  • Step 1: Understand what 'a ≡ b (mod m)' means. It means that when you divide a and b by m, they leave the same remainder.
  • Step 2: Recognize that if a and b leave the same remainder when divided by m, then the difference (a - b) must be a multiple of m.
  • Step 3: Conclude that 'a - b' is divisible by m, which is the key idea behind modular arithmetic.
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