Solve the following modulo problems using repeated addition: −45 mod 8, −13 mod 3.

Here are the solutions for the modulo problems using repeated addition: 1. −45 mod 8 To find −45 8, we add 8 to −45 repeatedly until the result is between 0 and 7. We need to add 8 at least 45/8 = 5.625 = 6 times. −45 + (6 × 8) = −45 + 48 = 3; Therefore, −45 8 = 3. 2. −13 mod 3 To find $-

Solve the following modulo problems using repeated addition: −45 mod 8, −13 mod 3.

Here are the solutions for the modulo problems using repeated addition: 1. −45 mod 8 To find −45 8, we add 8 to −45 repeatedly until the result is between 0 and 7. We need to add 8 at least 45/8 = 5.625 = 6 times. −45 + (6 × 8) = −45 + 48 = 3; Therefore, −45 8 = 3. 2. −13 mod 3 To find $-

Solved: Solve the following modulo problems using repeated…

Here are the solutions for the modulo problems using repeated addition:

-45 mod 8 To find $-45 \pmod 8$ , we add 8 to $-45$ repeatedly until the result is between 0 and 7. We need to add 8 at least $\lceil \frac{45}{8} \rceil = \lceil 5.625 \rceil = 6$ times.
$-45 + (6 \times 8) = -45 + 48 = 3$
Therefore, $-45 \pmod 8 = \boxed{\text{3}}$ .
-13 mod 3 To find $-

Solve the following modulo problems using repeated addition: -45 mod 8, -13 mod 3.

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