What two numbers add up to 8009?

There are infinite combinations of two numbers that add up to 8009. Here are some examples using negative numbers:

-1 + 8010 = 8009
-2 + 8011 = 8009
-3 + 8012 = 8009
...

Here are some examples using two fractions that will add up to 8009:

8009/2 + 8009/2 = 8009
16018/3 + 8009/3 = 8009
24027/4 + 8009/4 = 8009
...

And here are some examples using two decimal numbers that will add up to 8009:

1.25 + 8007.75 = 8009
2.50 + 8006.5 = 8009
3.75 + 8005.25 = 8009
...

As you can see from the lists above, it can go on forever. However, when answering "What two numbers add up to 8009?", 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 8009. (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 8009?" has 4004 answers:

1 + 8008 = 8009
2 + 8007 = 8009
3 + 8006 = 8009
.
.
4002 + 4007 = 8009
4003 + 4006 = 8009
4004 + 4005 = 8009

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 8009 by 2 and then rounded down to the nearest whole number if necessary.

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