# Jake Lai's Problem

**Number Theory**Level 5

\[A=\left[ \prod _{ p=6k+1 \text{ is prime, } p>3 } (1+p^{ -1 }) \right] \left[ \prod _{ p=6k-1 \text{ is prime, }p>3 } (1-p^{ -1 }) \right] \]

Find the value of \(\left\lfloor 100000A \right\rfloor \).

**Clue**: Use the Legendre symbol and the fact that it is completely multiplicative.