Fun fact: that fact about prime rows of Pascal's triangle is actually if and only if. All elements of the n'th row of pascals triangle apart from the 1s at the end are divisible by n if and only if n is a prime. Proving the other direction is a little bit harder but it's fun imo
@@MihaiNicaMath A friend told me he had spotted this pattern, wasn't sure if it was true and hadn't tried to prove it. I later found the same result in this numberphile video: th-cam.com/video/HvMSRWTE2mI/w-d-xo.html
@@henryginn7490 Wow nice find! Is the main contribution in that paper then the way to speed it up? Or was it genuinely only discovered recently that n is a prime if and only if the n-th row is all zeros mod n?
@@henryginn7490 I ended up going down a rabbit hole with this and I made a whole follow up video about this! The if and only isnt new but the trick to reduce to poly time is from early 2000s th-cam.com/video/gFMHlDqOPIk/w-d-xo.html
Thanks!!! Its partially because I don't post very regularly....if you want an alert when I do post something you should subscribe with the bell to get notifications.
The quality of this video made me doubt the quality of TH-cam's recommendation algorithm
@@elorating haha thank you so much! I was also quite disappointed this one didn't get picked up more.
Fun fact: that fact about prime rows of Pascal's triangle is actually if and only if. All elements of the n'th row of pascals triangle apart from the 1s at the end are divisible by n if and only if n is a prime. Proving the other direction is a little bit harder but it's fun imo
Cool! I didn't know that, will try it out! I suppose it might be related to the fact there are no zeros at all in the stencil until the p-th row
@@MihaiNicaMath A friend told me he had spotted this pattern, wasn't sure if it was true and hadn't tried to prove it. I later found the same result in this numberphile video: th-cam.com/video/HvMSRWTE2mI/w-d-xo.html
@@henryginn7490 Wow nice find! Is the main contribution in that paper then the way to speed it up? Or was it genuinely only discovered recently that n is a prime if and only if the n-th row is all zeros mod n?
@@MihaiNicaMath I have no idea! I would be surprised if it wasn't spotted earlier
@@henryginn7490 I ended up going down a rabbit hole with this and I made a whole follow up video about this! The if and only isnt new but the trick to reduce to poly time is from early 2000s th-cam.com/video/gFMHlDqOPIk/w-d-xo.html
It's visually very pleasing to see how a Pascal's Triangle of Mod X is shown from the first X rows of the triangle.
Thank you!!!
This video is great, shocked you've got so few subscribers!
Thanks!!! Its partially because I don't post very regularly....if you want an alert when I do post something you should subscribe with the bell to get notifications.
Oh, that’s what it’s called…