For any a and b(both positive integers not equal to each other), can functions having the below properties exist? If no, why not?
f(a,b) = Z
g(a) = Z
h(b) = Z
Z is the common output of all these functions. Please also note that for each unique pair of (a,b) we get a unique Z.
More generally,
f(a,b,c,..) = Z
g(a) = Z
h(b) = Z
i(c) = Z
...
...
I am not a mathematician and I don't really know which tags should be used in this question so please pardon me if you see this question or its tags as irrelevant.
No you can’t.
If you take a pair of values $(a_0,b_0)$ then $f(a_0,b_0) = g(a_0)$ now if you change the value of b $(a_0,b_1)$ then $f(a_0,b_1) \ne f(a_0,b_0)$ by your requirement for unique values.
But since $f(a_0,b_1) = g(a_0)$ then $g(a_0) \ne g(a_0)$ which is absurd.
Basically since g and h have no knowledge of the other parameter to f there is no way it can change according to it.