You assume that all the time Hugo.
It is this constant assumption that annoys other people so much.
You did not answer the question. If you were looking at the AOPS question then you did not even TRY to answer this question by yourself.
The AOPS question or the answer should not have been anywhere near you!
For a question like this you can check your answer from the original question given. You did not need to look anywhere else for confirmation, even when you were challenged, you did not check your answer thoroughly.