In a modular arithmetic system, if 8 is congruent to 2 modulo n, what can be con

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Question: In a modular arithmetic system, if 8 is congruent to 2 modulo n, what can be concluded about n?

Options:

Correct Answer: n must be a factor of 6

Solution:

Since 8 - 2 = 6, n must be a divisor of 6.

In a modular arithmetic system, if 8 is congruent to 2 modulo n, what can be concluded about n?

In a modular arithmetic system, if 8 is congruent to 2 modulo n, what can be concluded about n?

Step 1: Understand what 'congruent modulo n' means. It means that when you subtract the two numbers (8 and 2), the result should be divisible by n.
Step 2: Calculate the difference between the two numbers: 8 - 2 = 6.
Step 3: Since 8 is congruent to 2 modulo n, this means that n must divide the difference, which is 6.
Step 4: Identify the divisors of 6. The divisors of 6 are 1, 2, 3, and 6.
Step 5: Conclude that n can be any of the divisors of 6 (1, 2, 3, or 6).

Modular Arithmetic – Understanding congruences and their implications in terms of divisibility.
Divisibility – Recognizing that if a number is congruent to another modulo n, the difference must be divisible by n.