Years ago, I watched this YouTube video. At 17:30, the professor said that the smallest integer solution to $313(x^3+y^3)=z^3$ has more than $1000$ digits!
I remembered this today and I was curious to see the $1000$-digit solution and how it was even possible to find such a thing. However, after hours of searching, I found nothing.
I would like to ask for a reference about this theorem. Who discovered it, how did they discover it, and what is the $1000$-digit solution?
asked one of my friends who has a master's degree in mathematics and he was also surprised by this fact. So I decided to ask this question here.