Graham’s conjecture (1971): Modulo some prime p, can you find a way to order any subset of {1,...,p-1} so that its successive partial sums are all distinct?
www.quantamagazine.org/mathematicia...
quantamagazine.org
Mathematicians Harness Randomness To Crack a 55-Year-Old Conjecture | Quanta Magazine
After a long hiatus, the problem, which was likely inspired by juggling, has finally been resolved by a group of young mathematicians.