Integers

Integers in Ren'Py and Python are whole numbers of unlimited precision. Obvious uses are counting things, but they can also be used for state tracking.
See Python 3 Numeric types: int 

They aren't tied to a hardware specific number of bits which is quite unusual if you've come from other languages that where an int is a primitive type. Integers, like everything else in Python, are objects. There's no equivalent to MAX_INT or Integer.MAX to worry about.

Division

While all the usual mathematical operators work as you'd expect with integers we need to talk about division. Integer division works differently in Python 2 and Python 3, and thus between Ren'Py 7.x and Ren'Py 8.x.

Ren'Py 7 / Python 2

Dividing one integer by another using / gives an integer result, as does using //. The result is always rounded down to negative infinity. If you need a floating point result you need to convert one of the operands to a float first.

> 3 / 2
1
> 3 // 2
1
> (-3) / 2
-2
> float(3) / 2
1.5

Ren'Py 8 / Python 3

Dividing one integer by another using / always gives a floating point result. Dividing one integer by another using // gives an integer result. The result is always rounded down to negative infinity.

> 3 / 2
1.5
> 3 // 2
1
> (-3) / 2
-1.5
> (-3) // 2
-2

To be compatible across both versions use the // operator for integer division. For compatible floating point division use float(x) / y.

Modulus

The modulus operator % works alongside the integer division operator //. For positive dividends this is the same as the remainder:

> 5 // 3
1
> 5 % 3
2

If you need both the result of a division and the modulus then Python has the divmod function:

    dollars, cents = divmod(costCents, 100)

Bitwise operations

Bitwise operations are only available on integers. These work as though on a two's complement version of the number, with as many bits as needed. In a visual novel these are likely only useful for puzzles.

Integer Literals

Integer literals can be specified in decimal, binary, octal, or hexadecimal.
See Integer literals  (Python 2) 

Note: Python 2 allows a postfix of l or L to indicate a value larger than a 32-bit integer, but this is largely redundant as values outside this range are automatically treated as being "long".