For any n+1 integers, some difference of two of them is divisible by n - Pigeonhole Principle
3Today we are going to see an application of the pigeonhole principle to divisibility (a number-theoretic claim). Watch carefully how in the proof the pigeonhole principle gives us numbers to play around with! We use the Quotient-Remainder Theorem to do a lot of heavy lifting for us!
Time Stamps:
0:00 Opening, background on divisibility and Quotient-Remainder Theorem
3:57 Given any set of n+1 integers, there are two of them whose difference is divisible by n (full proof)
19:40 Summary
21:26 Closing
Have a beautiful day!
Supporters (to date of publication, by tier (top to bottom)):
----------------------------------------------------------
Patreon Supporters (General Support):
Draikou
Patreon Supporters (Basic Support):
Patreon Supporters (Supporter Access!):
Eric R
-----------------------------------------------------------
Become a supporter today! To support my work and mission to provide free or accessible Computer Science education (especially in theory), subscribe to the channel, share my videos. Please donate and contribute to support my work for more content:
PATREON: https://www.patreon.com/PageWizard
SUBSCRIBESTAR: https://www.subscribestar.com/drpage
PAYPAL: https://paypal.me/pagewizard
Follow also at:
FACEBOOK: https://www.facebook.com/DanielRPage
TWITTER: https://twitter.com/PageWizardGLE
QUORA: https://www.quora.com/profile/Daniel-R-Page
TWITCH: https://www.twitch.tv/pagewizard
#ComputerScience
#combinatorics
#numbertheory