What two numbers add up to 4012?

There are infinite combinations of two numbers that add up to 4012. Here are some examples using negative numbers:

-1 + 4013 = 4012
-2 + 4014 = 4012
-3 + 4015 = 4012
...

Here are some examples using two fractions that will add up to 4012:

4012/2 + 4012/2 = 4012
8024/3 + 4012/3 = 4012
12036/4 + 4012/4 = 4012
...

And here are some examples using two decimal numbers that will add up to 4012:

1.25 + 4010.75 = 4012
2.50 + 4009.5 = 4012
3.75 + 4008.25 = 4012
...

As you can see from the lists above, it can go on forever. However, when answering "What two numbers add up to 4012?", 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 4012. (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 4012?" has 2006 answers:

1 + 4011 = 4012
2 + 4010 = 4012
3 + 4009 = 4012
.
.
2004 + 2008 = 4012
2005 + 2007 = 4012
2006 + 2006 = 4012

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 4012 by 2 and then rounded down to the nearest whole number if necessary.

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What two numbers add up to 4013?
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