My MegaFavNumber: 61,218,182,743,304,701,891,431,482,520

A video about my MegafavNumber: 61,218,182,743,304,701,891,431,482,520

A bunch of Maths YouTubers have come together to create videos about their favourite numbers over one million, which we are calling MegaFavNumbers.


And we want *you*, the viewers, to join in. We want you to make your own video about your favourite meganumber. You can think of a cool big number, or think of a cool topic first and hang a meganumber on it.


Upload your videos to YouTube with the hashtag #MegaFavNumbers and with MegaFavNumbers in the title. And your video will be added to the MegaFavNumbers playlist. Submit your videos anytime before Wednesday the 2nd of September to be added to the MegaFavNumbers playlist!


Links:
David Singmaster's proof is here: https://www.fq.math.ca/Scanned/13-4/s...


My python code for the initial search is here: https://github.com/zoelgriffiths/pascals


Notes on the algebraic manipulation for the search for integer solutions to (n+1)Cr = nC(r+1), and on using the Fibonacci expressions to generate integer solutions, are here: https://drive.google.com/file/d/18bFr...

(See if you can spot the factorial symbol that is in the wrong place in these notes...)

Clarifications:
04:30 - I'm counting the first row of Pascal's triangle as 'row 0'
04:45 - When I say 'that's not true of the other numbers', I'm saying unlike 120 and 210, I can't know for certain from my search that those other numbers appear exactly six times across the triangle.
08:33 - 3003 appears exactly eight times across the triangle.
Generally, when I’m talking about solutions to (n+1)Cr = nC(r+1), I’m talking about integer solutions.



Pascal's triangle image credit: Nonenmac at English Wikipedia