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In modular arithmetic, which of the following is true for any integer a?

Practice Questions

Q1
In modular arithmetic, which of the following is true for any integer a?
  1. a mod 1 = 0
  2. a mod a = 1
  3. a mod 0 is undefined
  4. a mod 2 = 0 or 1

Questions & Step-by-Step Solutions

In modular arithmetic, which of the following is true for any integer a?
  • Step 1: Understand what 'mod' means. 'a mod b' means the remainder when a is divided by b.
  • Step 2: Identify the value of b in this case. Here, b is 2.
  • Step 3: Recognize that any integer can be either even or odd.
  • Step 4: If a is even, when you divide it by 2, the remainder is 0. So, a mod 2 = 0.
  • Step 5: If a is odd, when you divide it by 2, the remainder is 1. So, a mod 2 = 1.
  • Step 6: Conclude that for any integer a, a mod 2 will always be either 0 (if a is even) or 1 (if a is odd).
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