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 A^2 = B^3 + C^3
 Set {4,b,c,d,e} such that the product of any two of them increased by 1 is a square
 smallest integer whose first n multiples all contain a 3
 Set {3,b,c,d,e} such that the product of any two of them increased by 1 is a square
 Set {2,b,c,d,e} such that the product of any two of them increased by 1 is a square
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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 $4r1$ 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.