Download Problem statement: Solution: Let`s note that is not a solution. That

Problem statement:
Solution:
Let’s note that
Placing
Since
in .
Replacing
is not a solution. That means that
such that
in the original equation, we get:
is constant and
generates all values, we get that
in the original equation:
Changing the values of
and
we get that:
Because the right sides are equal, the left sides must be equal, hence:
Replacing
Since
:
generates all values in , we get that:
Placing x=0 in the original equation, we get:
Cancelling terms, we get that
Replacing
.
.
in the original equation we get:
generates all values
…
Substituting the last equation in
:
Replacing
From
we have:
Substituting in the original equation we see that this solution satisfies the conditions given.
Special thanks to AOPS member obi1kenobi for helping solve this problem.