The TI-83 does not provide a mod() function, but it is programmable and it does provide the function int(), so we can write a simple program to compute b MOD m for any integer b and any positive integer m.

The built-in function int() returns the greatest integer less than or equal to its argument. Thus m*int(b/m) is always less than or equal to b, and the quantity

b-m*int(b/m)

is between 0 and b-1. Furthermore, b-(b-m*int(b/m)) is a multiple of m, so that b-m*int(b/m) is in fact equal to b MOD m.

To program this formula into the TI-83, we press to enter Program mode, then highlight NEW. The screen looks like this

We press and the calculator prompts for a name. Let's call this program "MOD." We type and the calculator prompts us for the first line of the program

The first line will be an Input statement. To enter an Input statement, we push again, then highlight I/O. The screen looks like this:

We press to select "Input," and then type in the rest of the line, using the ALPHA characters on the calculator keys. (The double quote is above the key and the space is above the key.) We press at the end of the line.

We enter the second line of the program in the same way.

The third and last line of the program will calculate and display the result. To get the Disp function, we press , highlight I/O, and press . To get the int() function, we press , highlight NUM, and press . Here is the finished program.

To use it, we first press to get out of Program mode. Then we press to get this screen

We press and the word prgmMOD appears. We press again, and our program prompts us for the number b. We enter a value for b, press , enter a value for m, and press again. The calculator gives us the answer.