siegelzero

I can recommend the book Guide to Graph Colouring: Algorithms and Applications by Lewis. It covers techniques including some state of the art methods for getting good but not provably optimal colorings. It discusses in depth local search and hybrid evolutionary algorithms, which tend to be the best performing on academic benchmarks (DIMACS graphs and large random graphs).

"Irresistible Integrals: Symbolics, Analysis and Experiments in the Evaluation of Integrals" - Boros and Moll

"Inside Interesting Integrals" - Nahin

And those who want to see trees go to r/marijuanaenthusiasts

There are some closely related difficult problems. Consider the fraction a/b, and let r be the length of the repeating fractional part. Then r <= b - 1. Moreover, if r == b - 1, then b is prime. In general, r divides phi(b), where phi is the Euler phi function.

I've solved 249 of them. I don't remember when I joined, but it must have been about 10 years ago. Solving PE problems was a great way to unwind in grad school (studying math) and learn some cool math in the process. There was a period where I was knocking them out pretty frequently, but I've only had the time to solve 4 problems in the past year.