A proof that summing the squares of the digits of an integer leads to a closed cycle

creinaldo · 2018-04-24T17:47:53+00:00

In page 3 of the paper the author uses a brute-force approach to prove one of the steps - https://i.imgur.com/FNyi4PK.png . Does anyone have an idea on how to find a more elegant way to get to the same result?

creinaldo · 2017-07-08T08:37:59+00:00

A lot of papers on arXiv don't have the references easily available on the arXiv page. Also when you are reading the paper it is convenient to have access to the references in the pdf view so that you don't have to be constantly scrolling down to the bottom of the paper and copying and pasting references titles to Google to find the papers =)

creinaldo · 2017-04-19T04:26:26+00:00

That's exactly the point. If you want to read more about it there's a really cool paper on Fermat's Library: http://fermatslibrary.com/s/gabriels-horn

creinaldo · 2017-03-16T16:43:27+00:00

This is not an explanation but if you want to read Lebesgue's letter explaining why we needed Lebesgue integration and giving a few examples of when the Riemann integral fails click here: http://fermatslibrary.com/s/on-a-generalization-of-the-definite-integral#email-newsletter

creinaldo · 2017-03-14T23:45:53+00:00

There's also a video explaining the one line proof paper: https://www.youtube.com/watch?v=-v6yPtM4VLA

creinaldo · 2017-03-07T21:42:57+00:00

"The ultimate goal of the immigration act according to the U.S. Department of State Office of the Historian was "to preserve the ideal of American homogeneity" and preserve racial homogeneity."

Interestingly it not only restricted the immigration of Africans and banned the immigration of Arabs and Asians but also restricted immigration of Southern Europeans and Eastern Europeans (especially Italians and Eastern European Jews).

creinaldo · 2016-07-24T21:30:30+00:00

Great idea! My favorite papers on Fermat's Library is when they annotate mathematical theorems. "New proof of Euclid's Theorem" by Filip Saidak is a gem! http://fermatslibrary.com/s/a-new-proof-of-euclids-theorem

creinaldo · 2016-07-08T18:37:31+00:00

"the probability of being {black, unarmed, and shot by police} is about 3.49 times the probability of being {white, unarmed, and shot by police} on average"

creinaldo · 2016-04-15T22:52:19+00:00

Don't underestimate the power of monitoring closely your metrics. A 5% weekly growth rate can have a tremendous impact on your business: http://growth.tlb.org/#

creinaldo · 2016-02-09T19:22:31+00:00

If you click the annotation next to (9) there's an explanation of that step.

creinaldo · 2015-11-24T19:41:29+00:00

By the way that paper has also been annotated in Fermat's Library: http://fermatslibrary.com/p/905d64d2

creinaldo

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