Lets make a "forum" like thing for "Functional Equations".

I will post a question here, the person who solves it, would post another question and so on.

Lets make it short and simple :)

**Question 1:**
Find all the functions \(f\colon\mathbb{Q} \to \mathbb{Q}\) such that
\[f(x+y) + f(x-y) = 2f(x) + 2f(y)\] for all rationals \(x,y\).

Note: The answer showed be accompanied with a valid proof.

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TopNewestThere is already a Fuctional Equations Contest going on. But I think that the contest is currently paused as there are three other contests going on currently. – Svatejas Shivakumar · 8 months, 3 weeks ago

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