Project Lab
Collaborative mathematical projects: open problems, proofs in progress, and working investigations. Pick up a thread or start your own.
You can work on a project alone or invite others in.
6 projects found · topic: egyptian-fractions
- [Demo] Writing 1 with odd unit fractions
Looking for the shortest sums of different odd unit fractions that equal 1. Nine terms so far. We want to know if seven is possible.
Find the shortest ways to write 1 as a sum of different unit fractions with odd denominators.
ActiveSeeking contributors - [Demo] Mei's notebook: greedy expansions
Mei's private notes on where the greedy algorithm for Egyptian fractions does badly.
Collect examples where the greedy algorithm for Egyptian fractions is far from the shortest expansion.
Active🔒 Private · invite only - [Demo] Distinct denominators for 4/n
The residue-class identities for 4/n can always be chosen with three different denominators when n ≥ 3.
Show the identities for 4/n can always be chosen with three different denominators.
Completed🔒 Private · invite only - [Demo] Sylvester's sequence and greedy expansions
Why the reciprocals of Sylvester's sequence 2, 3, 7, 43, 1807, … add up to exactly 1, and how fast.
Write up why the reciprocals of Sylvester's sequence sum to 1, and how quickly the partial sums approach it.
Paused - [Demo] Covering Erdős–Straus residue classes
We collect three elementary identities for 4/n = 1/x + 1/y + 1/z, use them to reduce the Erdős–Straus conjecture to primes p ≡ 1 (mod 24), and check every such prime below 100,000 by computer.
Reduce the Erdős–Straus conjecture to as few primes as elementary identities allow, and check what is left by computer.
Paper finished· 9d ago
Search to 100,000 done· 26d ago
Completed - [Demo] A short note on 2/n
2/n is always a sum of two different unit fractions once n ≥ 3. A warm-up before the 4/n project.
Show that 2/n is always a sum of two different unit fractions for n ≥ 3.
Archived