What two numbers add up to 9905?

There are infinite combinations of two numbers that add up to 9905. Here are some examples using negative numbers:

-1 + 9906 = 9905
-2 + 9907 = 9905
-3 + 9908 = 9905
...

Here are some examples using two fractions that will add up to 9905:

9905/2 + 9905/2 = 9905
19810/3 + 9905/3 = 9905
29715/4 + 9905/4 = 9905
...

And here are some examples using two decimal numbers that will add up to 9905:

1.25 + 9903.75 = 9905
2.50 + 9902.5 = 9905
3.75 + 9901.25 = 9905
...

As you can see from the lists above, it can go on forever. However, when answering "What two numbers add up to 9905?", 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 9905. (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 9905?" has 4952 answers:

1 + 9904 = 9905
2 + 9903 = 9905
3 + 9902 = 9905
.
.
4950 + 4955 = 9905
4951 + 4954 = 9905
4952 + 4953 = 9905

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 9905 by 2 and then rounded down to the nearest whole number if necessary.

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