Siam's inequality

Algebra Level 3

What is the minimum integer value of \(x\) that satisfies the equation

\[\lfloor{\sqrt{x}}\rfloor - \lfloor{\sqrt{x+34}}\rfloor=0 ? \]

This problem is posed by Siam H.

Details and assumptions

The function \(\lfloor x \rfloor: \mathbb{R} \rightarrow \mathbb{Z}\) refers to the greatest integer smaller than or equal to \(x\). For example \(\lfloor 2.3 \rfloor = 2\) and \(\lfloor -5 \rfloor = -5\).


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