Final answer:
A reduced residue system modulo 28 comprises the numbers that are coprime to 28: 1, 3, 5, 9, 11, 13, 15, 17, 19, 23, 25, and 27. The value of θ(28) is 12, which represents the count of positive integers up to 28 that are relatively prime to it.
Step-by-step explanation:
To find a reduced residue system modulo 28, we are looking for a set of integers that are relatively prime to 28 and smaller than 28. The positive integers that are relatively prime to 28 (which means they share no common divisors with 28 other than 1) can be found by eliminating all multiples of 2 and 7, since 28 is divisible by these two prime numbers
A reduced residue system modulo 28 can be formed by the numbers that are coprime to 28: 1, 3, 5, 9, 11, 13, 15, 17, 19, 23, 25, and 27.
As for the value of θ(28), which is the Euler's totient function, it counts the positive integers up to a given integer n that are relatively prime to n. We can calculate this by noting that 28 = 2³ × 7, and applying the totient function properties, we have:
θ(28) = 28 × (1 - 1/2) × (1 - 1/7) = 28 × 1/2 × 6/7 = 12
Thus, there are 12 integers that form a reduced residue system modulo 28, and the value of θ(28) is 12.