What two numbers add up to 4098?

There are infinite combinations of two numbers that add up to 4098. Here are some examples using negative numbers:

-1 + 4099 = 4098
-2 + 4100 = 4098
-3 + 4101 = 4098
...

Here are some examples using two fractions that will add up to 4098:

4098/2 + 4098/2 = 4098
8196/3 + 4098/3 = 4098
12294/4 + 4098/4 = 4098
...

And here are some examples using two decimal numbers that will add up to 4098:

1.25 + 4096.75 = 4098
2.50 + 4095.5 = 4098
3.75 + 4094.25 = 4098
...

As you can see from the lists above, it can go on forever. However, when answering "What two numbers add up to 4098?", 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 4098. (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 4098?" has 2049 answers:

1 + 4097 = 4098
2 + 4096 = 4098
3 + 4095 = 4098
.
.
2047 + 2051 = 4098
2048 + 2050 = 4098
2049 + 2049 = 4098

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 4098 by 2 and then rounded down to the nearest whole number if necessary.

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What two numbers add up to 4099?
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