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If 4x ≡ 8 (mod 12), what is the smallest non-negative integer solution for x?

Practice Questions

Q1
If 4x ≡ 8 (mod 12), what is the smallest non-negative integer solution for x?
  1. 0
  2. 1
  3. 2
  4. 3

Questions & Step-by-Step Solutions

If 4x ≡ 8 (mod 12), what is the smallest non-negative integer solution for x?
  • Step 1: Start with the equation 4x ≡ 8 (mod 12).
  • Step 2: Understand that this means 4x - 8 is a multiple of 12.
  • Step 3: To simplify, divide both sides of the equation by 4. This gives us x ≡ 2 (mod 3).
  • Step 4: The equation x ≡ 2 (mod 3) means that when x is divided by 3, the remainder is 2.
  • Step 5: The smallest non-negative integer that satisfies this condition is 2.
  • Modular Arithmetic – Understanding how to manipulate equations under a modulus, including division and finding equivalent classes.
  • Divisibility – Recognizing when it is valid to divide both sides of a modular equation by a number.
  • Finding Solutions – Identifying the smallest non-negative integer that satisfies the modular equation.
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