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

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Question: In modular arithmetic, which of the following is true for any integer k?

Options:

  1. k mod 1 = 0
  2. k mod k = 1
  3. k mod 0 is undefined
  4. k mod k = 0

Correct Answer: k mod k = 0

Solution: 

For any integer k, k mod k = 0, as k is divisible by itself.

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

Practice Questions

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

Questions & Step-by-Step Solutions

In modular arithmetic, which of the following is true for any integer k?
  • Step 1: Understand what 'mod' means. 'k mod k' means we are finding the remainder when k is divided by k.
  • Step 2: Remember that any number divided by itself equals 1, with no remainder. For example, 5 divided by 5 equals 1.
  • Step 3: Since there is no remainder when k is divided by k, we can say that the remainder is 0.
  • Step 4: Therefore, for any integer k, the result of k mod k is always 0.
  • Modular Arithmetic – Modular arithmetic involves the remainder when one integer is divided by another, often expressed as 'a mod b'.
  • Divisibility – An integer k is divisible by itself, which means k mod k equals 0.
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