\[ \large \displaystyle\int _{ 0 }^{ 1 }{ \displaystyle\int _{ 0 }^{ 1 }{ x\left\{ \dfrac { 1 }{ 1-xy } \right\} \, dx\; dy } } =A-\dfrac { \zeta (B) }{ C } \]

If the equation above holds true for positive integers \(A,B\) and \(C\), find \(A\times B \times C\).

**Notations**:

\( \{ \cdot \} \) denotes the fractional part function.

\(\zeta(\cdot) \) denotes the Riemann zeta function.

×

Problem Loading...

Note Loading...

Set Loading...