In a certain modular arithmetic system, if 7 is congruent to 3 modulo 4, which of the following statements is true?
Practice Questions
1 question
Q1
In a certain modular arithmetic system, if 7 is congruent to 3 modulo 4, which of the following statements is true?
7 - 3 is divisible by 4
7 + 3 is divisible by 4
7 * 3 is divisible by 4
7 / 3 is divisible by 4
In modular arithmetic, if a ≡ b (mod m), then (a - b) is divisible by m. Here, 7 - 3 = 4, which is divisible by 4.
Questions & Step-by-step Solutions
1 item
Q
Q: In a certain modular arithmetic system, if 7 is congruent to 3 modulo 4, which of the following statements is true?
Solution: In modular arithmetic, if a ≡ b (mod m), then (a - b) is divisible by m. Here, 7 - 3 = 4, which is divisible by 4.
Steps: 5
Step 1: Understand what 'congruent' means in modular arithmetic. It means that two numbers have the same remainder when divided by a certain number (the modulus).
Step 2: Identify the numbers in the question. We have 7 and 3, and the modulus is 4.
Step 3: Calculate the difference between the two numbers: 7 - 3 = 4.
Step 4: Check if this difference (4) is divisible by the modulus (4). Since 4 divided by 4 equals 1, it is divisible.
Step 5: Conclude that since 7 - 3 is divisible by 4, the statement '7 is congruent to 3 modulo 4' is true.
