What two numbers add up to 7563?

There are infinite combinations of two numbers that add up to 7563. Here are some examples using negative numbers:

-1 + 7564 = 7563
-2 + 7565 = 7563
-3 + 7566 = 7563
...

Here are some examples using two fractions that will add up to 7563:

7563/2 + 7563/2 = 7563
15126/3 + 7563/3 = 7563
22689/4 + 7563/4 = 7563
...

And here are some examples using two decimal numbers that will add up to 7563:

1.25 + 7561.75 = 7563
2.50 + 7560.5 = 7563
3.75 + 7559.25 = 7563
...

As you can see from the lists above, it can go on forever. However, when answering "What two numbers add up to 7563?", 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 7563. (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 7563?" has 3781 answers:

1 + 7562 = 7563
2 + 7561 = 7563
3 + 7560 = 7563
.
.
3779 + 3784 = 7563
3780 + 3783 = 7563
3781 + 3782 = 7563

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 7563 by 2 and then rounded down to the nearest whole number if necessary.

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What two numbers add up to 7564?
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