Question

List five numbers that belong to the 5 (mod 6) numbers. Alternate phrasing, list five numbers that satisfy equation x = 5 (mod 6)

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Gerhard

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To find five numbers that belong to the set of numbers congruent to 5 modulo 6, we can start by finding the first number that satisfies the equation x = 5 (mod 6), and then incrementing by 6 to find the next numbers.

Step 1: Find the first number that satisfies x = 5 (mod 6)

To find the first number, we can substitute values for x until we find one that satisfies the equation.

Let's start with x = 5. When we divide 5 by 6, we get a quotient of 0 and a remainder of 5. Since the remainder is 5, we can say that 5 is congruent to 5 modulo 6. Therefore, 5 satisfies the equation x = 5 (mod 6).

Step 2: Increment by 6 to find the next numbers

To find the next numbers, we can add 6 to the previously found number and repeat the process.

Adding 6 to 5, we get 11. When we divide 11 by 6, we get a quotient of 1 and a remainder of 5. Therefore, 11 is congruent to 5 modulo 6.

Adding 6 to 11, we get 17. When we divide 17 by 6, we get a quotient of 2 and a remainder of 5. Therefore, 17 is congruent to 5 modulo 6.

Adding 6 to 17, we get 23. When we divide 23 by 6, we get a quotient of 3 and a remainder of 5. Therefore, 23 is congruent to 5 modulo 6.

Adding 6 to 23, we get 29. When we divide 29 by 6, we get a quotient of 4 and a remainder of 5. Therefore, 29 is congruent to 5 modulo 6.

Answer:

The five numbers that belong to the set of numbers congruent to 5 modulo 6 are:

5, 11, 17, 23, 29

Step 1: Find the first number that satisfies x = 5 (mod 6)

To find the first number, we can substitute values for x until we find one that satisfies the equation.

Let's start with x = 5. When we divide 5 by 6, we get a quotient of 0 and a remainder of 5. Since the remainder is 5, we can say that 5 is congruent to 5 modulo 6. Therefore, 5 satisfies the equation x = 5 (mod 6).

Step 2: Increment by 6 to find the next numbers

To find the next numbers, we can add 6 to the previously found number and repeat the process.

Adding 6 to 5, we get 11. When we divide 11 by 6, we get a quotient of 1 and a remainder of 5. Therefore, 11 is congruent to 5 modulo 6.

Adding 6 to 11, we get 17. When we divide 17 by 6, we get a quotient of 2 and a remainder of 5. Therefore, 17 is congruent to 5 modulo 6.

Adding 6 to 17, we get 23. When we divide 23 by 6, we get a quotient of 3 and a remainder of 5. Therefore, 23 is congruent to 5 modulo 6.

Adding 6 to 23, we get 29. When we divide 29 by 6, we get a quotient of 4 and a remainder of 5. Therefore, 29 is congruent to 5 modulo 6.

Answer:

The five numbers that belong to the set of numbers congruent to 5 modulo 6 are:

5, 11, 17, 23, 29

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