What two numbers add up to 2255?

There are infinite combinations of two numbers that add up to 2255. Here are some examples using negative numbers:

-1 + 2256 = 2255
-2 + 2257 = 2255
-3 + 2258 = 2255
...

Here are some examples using two fractions that will add up to 2255:

2255/2 + 2255/2 = 2255
4510/3 + 2255/3 = 2255
6765/4 + 2255/4 = 2255
...

And here are some examples using two decimal numbers that will add up to 2255:

1.25 + 2253.75 = 2255
2.50 + 2252.5 = 2255
3.75 + 2251.25 = 2255
...

As you can see from the lists above, it can go on forever. However, when answering "What two numbers add up to 2255?", 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 2255. (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 2255?" has 1127 answers:

1 + 2254 = 2255
2 + 2253 = 2255
3 + 2252 = 2255
.
.
1125 + 1130 = 2255
1126 + 1129 = 2255
1127 + 1128 = 2255

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 2255 by 2 and then rounded down to the nearest whole number if necessary.

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What two numbers add up to 2256?
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