Is a public getter and a private setter with same name possible in C#?

Question

How can I create a public getter and a private setter for a property? Is the following correct?

public String Password
{
    set { this._password = value; }
}

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Answer 1

public String Password
{
    private set { this._password = value; }
    get { return this._password; }
}

or you can use an auto-implemented property:

public String Password { get; private set; }