What two numbers add up to 8563?

There are infinite combinations of two numbers that add up to 8563. Here are some examples using negative numbers:

-1 + 8564 = 8563
-2 + 8565 = 8563
-3 + 8566 = 8563
...

Here are some examples using two fractions that will add up to 8563:

8563/2 + 8563/2 = 8563
17126/3 + 8563/3 = 8563
25689/4 + 8563/4 = 8563
...

And here are some examples using two decimal numbers that will add up to 8563:

1.25 + 8561.75 = 8563
2.50 + 8560.5 = 8563
3.75 + 8559.25 = 8563
...

As you can see from the lists above, it can go on forever. However, when answering "What two numbers add up to 8563?", 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 8563. (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 8563?" has 4281 answers:

1 + 8562 = 8563
2 + 8561 = 8563
3 + 8560 = 8563
.
.
4279 + 4284 = 8563
4280 + 4283 = 8563
4281 + 4282 = 8563

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 8563 by 2 and then rounded down to the nearest whole number if necessary.

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What two numbers add up to 8564?
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