What two numbers add up to 4163?

There are infinite combinations of two numbers that add up to 4163. Here are some examples using negative numbers:

-1 + 4164 = 4163
-2 + 4165 = 4163
-3 + 4166 = 4163
...

Here are some examples using two fractions that will add up to 4163:

4163/2 + 4163/2 = 4163
8326/3 + 4163/3 = 4163
12489/4 + 4163/4 = 4163
...

And here are some examples using two decimal numbers that will add up to 4163:

1.25 + 4161.75 = 4163
2.50 + 4160.5 = 4163
3.75 + 4159.25 = 4163
...

As you can see from the lists above, it can go on forever. However, when answering "What two numbers add up to 4163?", 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 4163. (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 4163?" has 2081 answers:

1 + 4162 = 4163
2 + 4161 = 4163
3 + 4160 = 4163
.
.
2079 + 2084 = 4163
2080 + 2083 = 4163
2081 + 2082 = 4163

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 4163 by 2 and then rounded down to the nearest whole number if necessary.

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What two numbers add up to 4164?
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