The set of integers {gcd(p, z) : z ∈ Z} where p is a prime number will contain only two elements: 1 and p.

Here's why:

1. If z is a multiple of p, then gcd(p, z) = p.
2. If z is not a multiple of p, then gcd(p, z) = 1. This is because p is a prime number and has no other divisors except 1 and itself.

So, the set {gcd(p, z) : z ∈ Z} = {1, p}.

Question

The set of integers {gcd(p, z) : z ∈ Z} where p is a prime number will contain only two elements: 1 and p.

Here's why:

1. If z is a multiple of p, then gcd(p, z) = p.
2. If z is not a multiple of p, then gcd(p, z) = 1. This is because p is a prime number and has no other divisors except 1 and itself.

So, the set {gcd(p, z) : z ∈ Z} = {1, p}.

Knowee AI · Accepted Answer

The set of integers {gcd(p, z) : z ∈ Z} where p is a prime number will contain only two elements: 1 and p.

Here's why:

1. If z is a multiple of p, then gcd(p, z) = p.
2. If z is not a multiple of p, then gcd(p, z) = 1. This is because p is a prime number and has no other divisors except 1 and itself.

So, the set {gcd(p, z) : z ∈ Z} = {1, p}.

uppose p is a prime number. Find all integers in {gcd(p, z) : z ∈ Z}

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