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Any positive number can be written as a sum of three palindromes

somethingorotherwhatever.com

41–50 of 114 posts

Re: Any positive number can be written as a sum of three palindromes

#41
post #23

Earlier quoted context omitted.

he was sarcastic...

I don't think it was sarcasm but they were making the same point. It's whimsical and excited and uncool . This will get you cachet among mathematicians though :)

Fortunately I don't have to go back and use this website time after time, which would get annoying.

But as a one-shot, I love it!

Re: Any positive number can be written as a sum of three palindromes

#43
post #25

Earlier quoted context omitted.

Would you prefer 11111+11111+33333 instead?

Still a bit boring, feels like cheating, something like 12321 + X + Y would be nice.

55555 = 12321 + 43234 + 0

:)

And if you don't like that:

55555 = 12321 + 23132 + 20102

Palindromes are sort of the least surprising numbers to have this property because you can easily "split" them into as many palindromes as you want like this. The surprising result is that you could write something like 19837100018374 as the sum of only 3 palindromes.

Re: Any positive number can be written as a sum of three palindromes

#44

Looks like code is at [0]. Didn't read in detail, but how difficult is it to find these 3 palindromes for something like a 100 digit number? Or, asked another way, how hard will it be to crack my new 3-palindrome-sum-factor based encryption scheme (assuming I have rules about not having easy factors)? 0 - https://github.com/christianp/sum-of-palindromes

Uniqueness would be a problem. The sum isn't guaranteed to have unique terms. 2 is (2,0,0) and (1,1,0).

Asymmetric key encryption then! Just replace Modulus(x,y) with this instead.

Re: Any positive number can be written as a sum of three palindromes

#45
post #41
post #23

Earlier quoted context omitted.

I don't think it was sarcasm but they were making the same point. It's whimsical and excited and uncool . This will get you cachet among mathematicians though :)

Fortunately I don't have to go back and use this website time after time, which would get annoying. But as a one-shot, I love it!

Exactly. This is effectively a hotsite for their proof.

Re: Any positive number can be written as a sum of three palindromes

#46
post #30

Earlier quoted context omitted.

Is there such a thing as "interactive nonfiction"? Because if not, there should be. Design educational websites this way and watch children learn.

> Is there such a thing as "interactive nonfiction"? The real physical Universe is interactive nonfiction.

The real physical universe doesn't offer tooling for playing with advanced math, though.

Re: Any positive number can be written as a sum of three palindromes

#49
post #30
post #9

Wonderful wonderful website. What happends to quirky people like this when they leave university and enter the industry?

Is there such a thing as "interactive nonfiction"? Because if not, there should be. Design educational websites this way and watch children learn.

you should check out Brett Victor's (http://worrydream.com/) and Nicky Case's (https://ncase.me/) websites. They both build really interesting systems for exploratory learning.
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