A Pythagorean triplet is a set of three natural numbers, a b c, for which,

a² + b² = c² For example, 3² + 4² = 9 + 16 = 25 = 5².

There exists exactly one Pythagorean triplet for which a + b + c = 1000. Find the product abc.

很直接

假设 \(a \leqslant b \leqslant c\) ,则

\begin{eqnarray} a \leqslant \frac{s-3}{3} \end{eqnarray} \begin{eqnarray} b < \frac{s-a}{2} \end{eqnarray}

31875000

Source:C++