លំហាត់ដកស្រងពី AoPs:
Let denote the set of all real numbers. Find all functions such that
Solution
The first step is to establish that . Putting , and , we get .
Also, , and .
We now evaluate two ways.
First, it is .
Second, it is . So , as required.
It follows immediately that , and .
Given any , let . Then , so .
Now given any positive , take so that .
Then .
Putting , we get . Hence .
It follows that and hold for all , .
Take any .
Let . If , then let .
If , then let and .
In either case we get some with .
But now take so that , then .
Contradiction. So we must have