Mapping two integers to one, in a unique and deterministic way

Question

Imagine two positive integers A and B. I want to combine these two into a single integer C.

There can be no other integers D and E which combine to C. So combining

Answer 1

It isn't that tough to construct a mapping:

   1  2  3  4  5  use this mapping if (a,b) != (b,a)
1  0  1  3  6 10
2  2  4  7 11 16
3  5  8 12 17 23
4  9 13 18 24 31
5 14 19 25 32 40

   1  2  3  4  5 use this mapping if (a,b) == (b,a) (mirror)
1  0  1  2  4  6
2  1  3  5  7 10
3  2  5  8 11 14
4  4  8 11 15 19
5  6 10 14 19 24


    0  1 -1  2 -2 use this if you need negative/positive
 0  0  1  2  4  6
 1  1  3  5  7 10
-1  2  5  8 11 14
 2  4  8 11 15 19
-2  6 10 14 19 24

Figuring out how to get the value for an arbitrary a,b is a little more difficult.