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We will be featuring different members of the Brilliant community, so that you can get to know them better. For the ninth issue, we are featuring Michael Mendrin, who is ...

Find all functions \( f(x) : \mathbb{R} \rightarrow \mathbb{R} \) which satisfy

\[f(x+y) = f(x) + f(y)+2xy.\]

Hint: If \(r\) is a rational number, what can we ...

For some \(m\in\mathbb N\), there are \(2^m\) positive real numbers written on a board product of which is \(1\). At each step, we can choose two numbers ...

Given that \(a,b\in\Bbb{Z}^+\) and \(\gcd(a,b)=1\).

Prove the following:

...

For some positive reals satisfying \(\displaystyle{ \sum_{i=1}^{24} x_i=1}\), determine the maximum possible value of ...

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