# About

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Thanks. I’m glad you enjoyed my posts

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!

Thanks kindly. I’m not famous.

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

No, I haven’t watched the videos

Any progress on Erdős–Straus conjecture ? Thank you/

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

Four ? Hungry algoritm gives exactly 4 distinct unit fractions.

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 $n+r$.

Take a look at

http://www.openproblemgarden.org/op/erdos_straus_conjecture

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