Question

Identify the integers that are congruent to 5 modulo 19. (Check all that apply.)

1) 0
2) 5
3) 10
4) 15
5) 20

Answer 1

The integer congruent to 5 modulo 19 is 5.

Step-by-step explanation:

An integer is congruent to 5 modulo 19 if it leaves a remainder of 5 when divided by 19. To identify the integers that satisfy this condition, we can start with 5 and keep adding or subtracting 19 until we find all the values.

1. 5 + 19 = 24 (not congruent to 5 modulo 19)
2. 5 - 19 = -14 (not congruent to 5 modulo 19)
3. -14 - 19 = -33 (not congruent to 5 modulo 19)
4. -33 + 19 = -14 (not congruent to 5 modulo 19)

Therefore, the only integer congruent to 5 modulo 19 is 5.