This post was originally posted by: Rijul Saini

I solved a cute functional equation today, and was also wondering what I was doing being a contributor here, so that resulted in this.

**IMO Short List 2002 A01**

Find all functions such that

*Solution*

Let denote the assertion .

Now,

Taking here, implies .

Now,

Taking here, implies .

Therefore, is onto i.e. covers all values of .

Now,let , and define a function as .

Therefore, our original assertion for changes into the equivalent assertion for , as being

As is onto, therefore is also onto. Also, . And then finally,

As is onto, therefore, covers all values of , and therefore, also covers all values of ,

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