I got stuck with my solution using fermat's little theorem but got that p=5 will work but could'nt prove why it will be the only answer. Your solution was very much elegant. I found another gem on yt, thanks yt algorithm :>
@letsthinkcritically3 жыл бұрын
Thank you!!
@СВЭП-и4ф10 ай бұрын
y^4 < p^x. for y > 4 p^x mod y = 4, p^x mod y^2 = 4. Not possible. => y
@joaquinfernandez92323 жыл бұрын
Sophie Germain likes this.
@debayuchakraborti19633 жыл бұрын
I can tell without watching the vdo how amazing its gonna be!! Thank You for doing this problem
@siddharthabhattacharya37873 жыл бұрын
Aap panditji faile hue ho
@letsthinkcritically3 жыл бұрын
Thank you for your support!!
@parthsingh35693 жыл бұрын
Well congratulations for qualifying IOQM all the best for INMO. Good job debayu
@debayuchakraborti19633 жыл бұрын
@@parthsingh3569 wowo thenks
@parthsingh35693 жыл бұрын
@@debayuchakraborti1963 may I know your score in ioqm?
@brinzanalexandru2150 Жыл бұрын
From the factorization we can write:y²-2y+2=p^a and y²+2y+2=p^b where obviously b>a and they are integers,if we divide both equations we get p^(b-a)=(y²+2y+2)/(y²-2y+2) now the fraction has to be an integer which is an easy exercise,we just do long division amd then get the inequality 4y≥y²-2y+2 which is satisfied only by y€[1,5] so after checking we conclude that only y=1 works but a trivial solution was y=0 which in my country is not considered as a natural number
@sheldoncooper54943 жыл бұрын
Wow u did this national level mathematics olympiad question with no hesistation and difficulty. I appriciate it and great work tho!! Could you pls tell me how to develope intuitive thinking to solve such problems.??
@debayuchakraborti19633 жыл бұрын
he is pro
@sheldoncooper54943 жыл бұрын
@@debayuchakraborti1963 ofc!!
@h4z4rd283 жыл бұрын
My tip is: start with basics and do A LOT of problems, then you can be also pro
@letsthinkcritically3 жыл бұрын
Try to remember the ‘moral’ of the problem, but not the steps. What I mean is how did you got through the bit you were stuck while solving the problems. It’s usually some non-trivial or uncommon tricks. Those tricks might be useful when you see problems of similar kind.
@pratikmaity43153 жыл бұрын
The name of your channel suits your videos
@shalvagang951 Жыл бұрын
I have found out one thing that when we factored out y^2+2y+2 and y^2+2-2y then their gcd is 1 relatively prime numbers so d is odd which divides them so d|4y d|y and so d|p^x but as d=1 so p^x, has a gcd of 1 so it means that 4y=p^b(p^a-b-1) then y cannot divide p^b and 4 cannot divide p^b as its odd it remains to one factor of 4y divide p^a-b-1
@satyamsaurav70053 жыл бұрын
Thanks for solving this problem.
@brettaspivey3 жыл бұрын
x^4 + 4 = 0 mod 5 which simplifies the proof a little
@jamesjames15492 жыл бұрын
Only if x and 5 are co-prime
@mariomestre7490 Жыл бұрын
Genial!!
@tonyhaddad13943 жыл бұрын
3:02 how ???
@karthikkrishnaswami31643 жыл бұрын
p|a and p|b => p|(a-b)
@perseus_07413 жыл бұрын
😍😍
@Gaming_639_ Жыл бұрын
5:05 what is V2 ?
@ittaloceara3 жыл бұрын
Nice
@letsthinkcritically3 жыл бұрын
Thank you!!
@Gaming_639_ Жыл бұрын
@@letsthinkcritically 5:05 what is V2(y^4+4) ?
@theandroidguy60323 жыл бұрын
I just Randomly sleceted x=y=1 and prime number as 5 and got answer but this didn't work every time 😅
@sumitsingh-bc1iw3 жыл бұрын
Can you please explain how we got that p can only be 2.? I understand that we had p^x=16(t) +4 but how do we ensure that p =2 is the only solution
@srivatsansriram83283 жыл бұрын
No no,it’s the greatest power of 2 is that 2 which means 4