Bounties

The following cash prizes are offered, payable by venmo or cryptocurrency or donation to a charity of your choice.

Cohomology of classical groups • $20

Write a python program to compute the complete (with torsion) integral cohomology ring of $\text{SO}(n)$ and $\text{U}(n)$. It should run reasonably fast, under a couple of minutes for $n=10$, and work for unbounded $n$. There should be a good justification, if not necessarily a proof, of why it is correct.

Finite groups of rotations • $20

Classify all the finite subgroups of $\text{O}\left(n\right)$ for every $n$. Reference for $n=5$.

Multiplicative order of $\mathrm{2,3}$ • $20

Prove or disprove that there are infinitely many prime numbers $p$ such that the multiplicative orders of $2$ and that of $3$ $\mathrm{mod}p$ are coprime. Such primes are sequence A344202.