Question

List five integers that are congruent to 4 modulo 12:

Answer 1

Five integers that are congruent to 4 modulo 12 are 4, 16, 28, -8, and 40, which all have a remainder of 4 when divided by 12.

Step-by-step explanation:

Integers that are congruent to 4 modulo 12 share the same remainder when divided by 12. This implies that when any such integer is divided by 12, the remainder is 4. To list five such integers, we can simply add or subtract multiples of 12 to the base integer 4.

• 4 (since 4 % 12 is 4)
• 16 (4 + 12 = 16, and 16 % 12 is 4)
• 28 (4 + 2×12 = 28, and 28 % 12 is 4)
• -8 (4 - 12 = -8, and -8 % 12 is 4 when we consider -8 as 4 modulo 12)
• 40 (4 + 3×12 = 40, and 40 % 12 is 4)

The process used here is to find numbers by adding or subtracting the modulus, in this case 12, to our initial number which is 4.