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1. benvitalis says:

Thanks. I’m glad you enjoyed my posts

2. I don’t even understand how I finished up right here,
but I assumed this publish was great. I do not recognise who
you’re but definitely you are going to a famous blogger should you are not already.
Cheers!

• benvitalis says:

Thanks kindly. I’m not famous.

3. Rob says:

I really enjoyed reading some of your posts. I’m currently fascinated with the x || y = x^2 + y^2 and generalizations (particularly the 1666…^3 + 5000…^3 + 3333…^3 pattern). It’s a somewhat similar phenomenon to Grafting Numbers (sqrt(5711) = 75.5711…) which I have written a paper about. I have an intro to that topic in my website link if you’re interested. Do you watch Numberphile on YouTube?

Cheers,
Rob

• benvitalis says:

No, I haven’t watched the videos

4. Eugene says:

Any progress on Erdős–Straus conjecture ? Thank you/

• benvitalis says:

Are you working on it? Have you also tried, for example, 4/n as the sum of four distinct unit fractions?

• Eugene says:

Four ? Hungry algoritm gives exactly 4 distinct unit fractions.

• Eugene says:

Just spent a couple of days on it. Looks hopeless.
I have found a lemma (unproved, but computationally looks true), which is stronger than the conjecture (with numerator 4).
Lemma.
For any natural \$n\$ there exists a natural \$r\$ such that \$4r-1\$ can be expressed a sum of 2 distinct factors of \$n+r\$.

• benvitalis says:
• Eugene says:

Thank you. I can see that the conjecture is still open.