Olympiad number theory: Suddenly a wild 7 appears!
Вставка
- Опубліковано 21 сер 2024
- We discuss INMO 2013 number theory problem in this video. Its quite surprising that the only prime that solves the equation is 7. Lets see how.
00:08 The question
00:50 Factorisation
02:45 Bezout type argument
03:06 The wild 7 appears.
04:22 Case analysis
07:24 Arithmetic mistake (see comment by @aminzahedim.7548)
08:40 Final answer
7:24 you made a slight mistake: if 4m+1=49, that means m=12 not 16. This would’ve already given you the solution you found not long after based on analyzing the last case; namely, m^2+3=3*49. Also, I think you brushed over the two key insights: a) the idea to take -3 to the LHS and factor the whole expression, and b) to use a very particular combination of 4m+1 and m^2+3 to arrive at a constant integer (independent of variable m), whence you could deduce something about their gcd. Eloquent explanation to a rather difficult problem, though. Thank you so much.
Oh... you are right about the mistake at 7:24. Looks like I am getting worse with arithmetic. Thank you for your comments.
Beautiful
Thank you.
Please start taking classes for ioqm on youtube
Your English is difficult to understand. I'm interested in this problem but it is too difficult to decipher your thick accent. I don't know if talking slower would help. I know it would make the video longer. Please enunciate more clearly in the future and maybe I'll subscribe. Thank you.
I have been told I speak fast. It is especially true that I do not enunciate properly (especially the last syllables). Thanks for the feedback, I will work on it.