What two numbers add up to 4137?

There are infinite combinations of two numbers that add up to 4137. Here are some examples using negative numbers:

-1 + 4138 = 4137
-2 + 4139 = 4137
-3 + 4140 = 4137
...

Here are some examples using two fractions that will add up to 4137:

4137/2 + 4137/2 = 4137
8274/3 + 4137/3 = 4137
12411/4 + 4137/4 = 4137
...

And here are some examples using two decimal numbers that will add up to 4137:

1.25 + 4135.75 = 4137
2.50 + 4134.5 = 4137
3.75 + 4133.25 = 4137
...

As you can see from the lists above, it can go on forever. However, when answering "What two numbers add up to 4137?", 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 4137. (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 4137?" has 2068 answers:

1 + 4136 = 4137
2 + 4135 = 4137
3 + 4134 = 4137
.
.
2066 + 2071 = 4137
2067 + 2070 = 4137
2068 + 2069 = 4137

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 4137 by 2 and then rounded down to the nearest whole number if necessary.

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What two numbers add up to 4138?
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