Find all functions such that
If there is exists such that then by (1) we have , so or . If there is not such then choose in (1) we have or
Setting in (1) we see that
In (2) if put we have
So in (2) choose then or .
In (2) choose then contradiction!
In (1) put we have So in (1) choose we see that
Now, in (1) choose then
By isn’t const, from (6) we have
From (5) and (7) we have
By (2),(8) and isn’t const we have .
In (1) choose then , contradiction!
Now, by checking direct (1) we have answer: