What two numbers add up to 2562?

There are infinite combinations of two numbers that add up to 2562. Here are some examples using negative numbers:

-1 + 2563 = 2562
-2 + 2564 = 2562
-3 + 2565 = 2562
...

Here are some examples using two fractions that will add up to 2562:

2562/2 + 2562/2 = 2562
5124/3 + 2562/3 = 2562
7686/4 + 2562/4 = 2562
...

And here are some examples using two decimal numbers that will add up to 2562:

1.25 + 2560.75 = 2562
2.50 + 2559.5 = 2562
3.75 + 2558.25 = 2562
...

As you can see from the lists above, it can go on forever. However, when answering "What two numbers add up to 2562?", 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 2562. (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 2562?" has 1281 answers:

1 + 2561 = 2562
2 + 2560 = 2562
3 + 2559 = 2562
.
.
1279 + 1283 = 2562
1280 + 1282 = 2562
1281 + 1281 = 2562

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 2562 by 2 and then rounded down to the nearest whole number if necessary.

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What two numbers add up to 2563?
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