Mathematical function to convert two numbers into one? Is there a mathematical function that converts two numbers into one so that the two numbers can always be extracted again?
Consider the map $$(x, y)\to 2^x3^y$$
For example, $$(\color{blue}{7}, \color{green}{3})\mapsto 2^\color{blue}{7}3^\color{green}{3} = 128\cdot27 = 3456.$$

To extract the original two numbers, divide 3456 by 2 and count how many times you can do this before you are left with an odd number: $$3456 \to 1728\to 864\to 432\to 216\to108\to 54\to 27$$  That's $\color{blue}{7}$ times.  Then divide 27 by 3 until you are left with 1: $$27\to9\to3\to 1$$ That's $\color{green}{3}$ times, so the original numbers were $\color{blue}{7}$ and $\color{green}{3}$.

Unlike the other answer in this thread, this works for any whole numbers, of unlimited size. But the process for extracting the original two numbers by this method is slow.
It is possible if you omit the condition "always". For example, for natural numbers $n,x,y \leq 10^n$  consider  the function $f(x,y)=10^{2n}x+y.$ It this case we are able  to extract $x$ and $y$  from $f(x,y).$