What two numbers add up to 8004?

There are infinite combinations of two numbers that add up to 8004. Here are some examples using negative numbers:

-1 + 8005 = 8004
-2 + 8006 = 8004
-3 + 8007 = 8004
...

Here are some examples using two fractions that will add up to 8004:

8004/2 + 8004/2 = 8004
16008/3 + 8004/3 = 8004
24012/4 + 8004/4 = 8004
...

And here are some examples using two decimal numbers that will add up to 8004:

1.25 + 8002.75 = 8004
2.50 + 8001.5 = 8004
3.75 + 8000.25 = 8004
...

As you can see from the lists above, it can go on forever. However, when answering "What two numbers add up to 8004?", it may be more interesting to set some criteria to limit the result. We will set the follow criteria:

1) Only positive whole numbers can add up to 8004. (0 is not a positive or negative number and should not be included.)

2) Since a+b=29 is the same as b+a=29, we should only list it once.

Now, the answer to "What two numbers add up to 8004?" has 4002 answers:

1 + 8003 = 8004
2 + 8002 = 8004
3 + 8001 = 8004
.
.
4000 + 4004 = 8004
4001 + 4003 = 8004
4002 + 4002 = 8004

We have truncated the list above due to space, but you may be interested to know that we calculated the number of answers by dividing 8004 by 2 and then rounded down to the nearest whole number if necessary.

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