User blog:Fejfo/Pythagorian Triple Ramsey Function

This is a fast growing function inspiered by a recent numberphile video . define \( \Pi(x) \) to be the minemum number \( N \) for which it is impossilbe to split all the numbers upto \( N \) in \( x \) groups without a group containing a pythagorian triplet.

\( \Pi(1)=5 \) because {1,2,3,4,5} contains the triplet \( 3²+4²=5² \)

The proof for \( \Pi(2)=7825 \) was outlined in the video.

It is unknown how fast this function grows. It's not even know if \( \Pi(3) \) is well-defined.