Write a short C++ function, isMultiple, that takes two positive long values, \(n\) and \(m,\) and returns true if and only if \(n\) is a multiple of \(m,\) that is, \(n=m i\) for some integer \(i\).

In this section, we will understand how to implement a function in C++. A function is a reusable block of code designed to perform a specific task. In C++, a function has a return type, a name, and a parameter list.
For the current exercise, we are writing a boolean function named `isMultiple` that checks if one number is a multiple of another. Here's how we start:

First, we define the function signature. The signature includes the return type (`bool`), the function name (`isMultiple`), and the parameters it takes. In this case, the parameters are two long integers, `n` and `m`.
The declaration looks like this:
`bool isMultiple(long n, long m);`

Second, we implement the function body. The body contains the logic needed to determine the multiple relationship between the two numbers. In this case, we will use the modulus operator, which is covered in the next section.
The complete implementation looks like this:
```cpp
bool isMultiple(long n, long m) {
return (n % m == 0);
}
```

The modulus operator (`%`) in C++ is used to find the remainder of a division between two integers. When you divide two numbers, the modulus operator gives you the remainder left over.
For example, `10 % 3` will yield `1`, because 10 divided by 3 is 3 with a remainder of 1.
In our specific case, the function aims to determine if `n` is a multiple of `m`. If `n % m` equals `0`, it means there is no remainder, and therefore, `n` is indeed a multiple of `m`.
In mathematical terms, if `n = m * i` for some integer `i`, then `n % m` will always be `0`.
Here's an example:
```cpp
bool isMultiple(long n, long m) {
return (n % m == 0);
}
```
In summary, the modulus operator helps us check for multiple relationships cleanly and efficiently.

In this section, we discuss boolean functions, which are functions that return a boolean value: `true` or `false`. These functions are instrumental in decision-making processes within programs.
The `isMultiple` function is a perfect example of a boolean function. It returns `true` if the condition is met (if `n` is a multiple of `m`), and `false` otherwise.
Boolean functions are particularly useful for:

• Condition checking
• Validation
• Controlling flow in loops and conditional statements

An important aspect to remember is that the function should perform a clear and specific check, and return `true` or `false` based on the check.
In our implementation, the boolean function `isMultiple` uses the result of the modulus operation to decide whether to return `true` or `false`. This makes the function both simple and efficient.
Here's our `isMultiple` function once again:
```cpp
bool isMultiple(long n, long m) {
return (n % m == 0);
}
```. This function reads easily and performs its task effectively, typical of good boolean function design.