Inspired by Me - 2

Calculus Level 4


\[S = \left(1- \dfrac{1}{2^4} \right) \left(1- \dfrac{1}{3^4} \right) \left(1- \dfrac{1}{5^4} \right) \left(1- \dfrac{1}{7^4} \right) \ldots\]

If the value of the above product \(S\) can be represented as \(\dfrac{A}{C \pi ^B}\), where \(A\), \(B\) and \(C\) are positive integers and \(A\), \(C\) are coprime to each other, find the value of \(A+B+C\).

Note: The product is taken over all primes, starting from \(2,3,5,7,\ldots\).

You may want to look up the Euler product formula to help you with this problem.


Problem Loading...

Note Loading...

Set Loading...