Fact : Ramanujan never gets bored he just counts till infinity.

@inyobill

2 жыл бұрын

Comes up with a finite sum, and proves the result by dividing by zero.

@Noam_.Menashe

2 жыл бұрын

He does ramnujan counting since it diverges.

@NightWanderer31415

2 жыл бұрын

To which infinity, though...

@asheep7797

2 жыл бұрын

He is the man who knows infinity, yes.

@chaurashwonsingkai3739

2 жыл бұрын

@@inyobill 😂

Proof by not knowing the rigorous method: So if x and y are natural, that means both of them must be perfect squares less than 11. Only options are then 1, 4 and 9. By the "proof of the keen eye" we can tell x and y must be 9 and 4 Q.E.D

@PapaFlammy69

2 жыл бұрын

:D

@pedrokrause7553

2 жыл бұрын

That's actually a really great thinking. More precisely, y ≤ 7 and x ≤ 11. Therefore, y ∈ [1,4] and x ∈ [1,4,9]. Because x≠y, these are the only possibilities to consider: x,y = 4,1 or 9,1 or 1,4 or 9,4 From which is easy to see that 9,4 is the solution.

@rhythmmandal3377

2 жыл бұрын

Elegant AF

@luckychouhan3393

2 жыл бұрын

What is the meaning of Q.E.D please tell me because I've seen Q.E.D written in many books and other PDFs. 😥

@thomy2562

2 жыл бұрын

@@luckychouhan3393 en.wikipedia.org/wiki/Q.E.D.

8:39 That part killed me out of laughter

@clusteringmiu

2 жыл бұрын

just fuck itself lmao

@ananthnm3014

2 жыл бұрын

ahahahah samee

@polotrav3439

2 жыл бұрын

Caught me off guard, I literally did a double take.

I seem to remember reading about this equation in "the man who knew infinity" (about Ramanujan obv) where a friend of his gave him this problem and Ramanujan quickly noticed that you can easily guess the solution by thinking of small enough perfect squares. He was still a young student at the time.

@thatkindcoder7510

2 жыл бұрын

Seems pretty smart, should probably consider becoming a mathematician

@adriansison1503

2 жыл бұрын

kek.

@kennytheripper2526

2 жыл бұрын

The prodigy

@sjs260563

2 жыл бұрын

either I also read this or I'm a genius, probably the former ;)

It’s sad to see only a few of your subscribers actually watch your videos with such great content!

@PapaFlammy69

2 жыл бұрын

ye :c

@heisenberg2415

2 жыл бұрын

yeah right

Ramanujan: In the title 100 000 Indians: Allow us to introduce ourselves Btw I really liked how you incorporated your sponsor into the video, that was so smooth ^^

@lgooch

2 жыл бұрын

They just never shut the fuck up

@padho4416

2 жыл бұрын

@@lgooch no we are here brother...

@vaibhavsrivastva1253

2 жыл бұрын

@@lgooch Problem?

@jackriver1999

2 жыл бұрын

Not Indian, bro, but Ramanujan is one of my heroes.

@prithwishsen4710

2 жыл бұрын

Tbh most Indians are either engineers or doctors very less are mathematicians

What a coincidence Yesterday only I watched the movie " the man who knew infinity"

@sahilbaori9052

2 жыл бұрын

The big tech is watching

Here is what I thought: since sqrt x+ y is 7, y must be less than 7. Since I assumed both were perfect squares, this means y is either 1 or 4. Assuming it's 1, looking at the second equation that would make nine 10, which is not a perfect square. But if y is 4, that makes x + 2=11. This makes x 9, which is a perfect square. It works in both equations, so x=9, y=4.

One could make an entire channel just going over Ramanujan's proofs and vibing.

“So this case can go fuck itself” This is why you’re the best lmaoo

Indian scammers after watching this video: Maybe we shouldn’t have annoyed Flammy that much.

@PapaFlammy69

2 жыл бұрын

xD

@banditapattanaik3179

2 жыл бұрын

🤣

@studynow6615

2 жыл бұрын

hope its just a joke because most of the indian viewers are pretty smart and not scammers

@JaceGameplay

2 жыл бұрын

@@studynow6615 i know english isn't your first language (nor even mine) but there's a critical difference between "indian scammers" and "indians are scammers". The first one refers to a subgroup of indians. Like, "between all indians, some of them are scammers". The second one that is a generalization. Anyway, it is a joke.

@mr.useless5103

2 жыл бұрын

@@JaceGameplay Study now guy comment wasn't about the difference between the two . I didn't get it why someone need to explain it ? My English is also not good .

I thought of a fun one to tackle this problem, using the sum of the first N natural numbers. First transform the system by using a = √x and b =√y. Subtract the second equation from the first and you get a^2 - a - (b^2 - b) = 4. Dividing both sides by 2 gives (a^2 - a)/2 - (b^2 - b)/2 = 2, which is the sum of the first a-1 natural numbers, subtract the first b-1 natural numbers. That be a telescoping sum, so we get the sum the natural numbers starting at b + 1 to a - 1 = 2. Then it gets a bit hand wavy, and we can say that 1 + 2 = 3, so that can't be it, so we can try - 1 + 0 + 1 + 2 = 2, which checks out. So we then get b + 1 = - 1 and then a - 1 = 2. Solving and then transforming back, we get x = 9 and y = 4. Ta da!

Srinivasa Ramnujan was one of the figures that Influenced me in my early life to pursue a career in computer science. Despite the restrictions on food, being a stranger in a foreign land,diseases etc. , his passion for math shined through. When we face difficulties in life, it is motivating to think about the difficulties he faced and draw courage and optimism from the sacrifice and example made by Ramanujan.

When he prounouces "y" as "wa" and "why" as "y"

I like how all of this is so simple that it could be taught in schools to enhance creativity.

5:10 I think what you meant was that the integers are a unique factorisation domain (ufd), which means that any element has a factorisation into primes (in the sense of ring theory). You might have confused it with Gauss‘s theorem that the polynomial ring of a ufd is itself a ufd.

@PapaFlammy69

2 жыл бұрын

I think you're right, sorry for the confusion! Been a while :p

0:00 Nice piss in that bottle. I loved the video! Keep up the great work

The diagram you have in the background is so beautiful. It just stays the pattern even if you keep zooming forever

Math puns are a sine of depression :(

@therealrealludwigvanbeethoven

2 жыл бұрын

Nice

I used the same method you did, with the only difference being I used the substitution s=√(x) and t=√(y) => s²=x and t²=y

Ramanujan is quite the legend. Awesome man!

8:39 "meaning this case right here can go fuck itself" hahaha. I love this dude

@PapaFlammy69

2 жыл бұрын

:D

He was not talking to ghosts he was talking to the godess of learning Namagiri.

Awesome and neat explanation! My friend gave me this problem, and I started by squaring both sides which made things pretty messy. However, would you mind telling why x should belong to Natural no.s? I didn't quite get that part

@PapaFlammy69

2 жыл бұрын

Because we want to solve a Diophantine Equation =)

8:40 didnt expect to laugh so hard

OH Flammy, you are my hero. I totally lost it laughing when you said that the fraction can go itself.

If x and y are natural numbers then sqrt(x)-sqrt(y) is not necessarily a natural number so when considering factors of 4 don't you have to consider irrational factors or rule them out somehow?

@dalek1099

2 жыл бұрын

Solved my own comment. Rearranging Equation 1: sqrt(x)=7-y which must be in natural numbers and Rearranging Equation 2: sqrt(y) =11-x which must be in natural numbers.

So y = woä? Never heard this pronounciation before.

5:19 Correct: stress on second syllable = noun, stress on third syllable = adjective.

I am not sure if my approach was correct, but I attacked this set of equations in a different manner. First, I rearranged first eqn to get y=7-sqrt(x), then I substituted that in to the second eqn, getting x + sqrt( 7 - sqrt(x) ) = 11. Second, I moved the x to RHS, squared both sides. Then isolated sqrt(x), then squared both sides again, getting: x = 49 - 14(11-x)^2 + (11-x)^4 Then I changed signs on both sides, added 11 so that I would get 11-x on LHS, then moved that to the other side. Setting 11-x = t, I got the following quartic polynomial: t^4 - 14t^2 + t + 38 = 0 It can be quickly noticed that t=2 satisfies the above polynomial equation; that factorized into: (t-2)(t^3 + 2t^2 - 10t - 19) = 0 It seems that 3 more real solutions exist (for t), accoring to WolframAlpha, but they are probably of no interest because they are non-integer. I might have made a mistake, though. Coming back from the substitution: 11-x=2 we get x=9 and y=4. I am curious how to tell if such a set of eqns has more than one integer solution. The numbers were nice in this case, but generally a quartic like above migth not be easily solvable, if at all in integers.

"This case right here can 08:41"

Love your content Papa!

interesting I solved the equation using a different method. Rearrange x+ sq root y = 11 to x= 11 - sq root y --> plug this into sq root x +y = 7 to get sq root (11- sq root y) + y = 7 --> minus y on both sides --> sq root (11- sq root y) = 7-y, afterwards square both sides --> 11- sq root y = (7-y)^2 , minus 11 on both sides and open (7-y)^2 --> - (sq root y)= y^2 -14y + 49 -11 --> - (sq root y)= y^2 -14y + 38, then square both sides once more, afterwards minus y on both sides --> y= y^4 -14y^3 + 38y^2 - 14y^3 + 196y^2 -532y+ 38y^2 -532y +1444 --> y^4 - 28y^3 + 272y^2 -1065y + 1444 =0 , I knew this had something to due with polynomial division, however due to me calculating just right as I saw the thumbnail I assumed that there were no natural factors because I knew a bit about Ramanujan, (the fact he was a mathematical genius born into the british raj) so I slapped this shit into symbolab because i assumed that he likes to challenge himself with the wildest shit ever and facepalmed after I received that one of the factors of y were 4. The other answer incase any of you are wondering the other answer that does not include imaginary numbers is y=9.80511.... , x ~ 7.868642

@emil8120

Жыл бұрын

I just notices a feature the cross out feature, i knew never youtube ran that, i'll leave it unedited, due to the fact that i don't think it really blockages information from being seen, and i have a general preference for unedited comments

Prove by intuition: its feels like x=9 and y=4

8:39 Well! didn't expect that!

Papa Flammy this was a nice video but I used to enjoy your previous videos much more as you used to do very difficult integrals but now you only do simple problems ( compared the previous ones ), please keep making videos on difficult ones too.

Solve the following: Beat Elden Ring

I do this in 2 minutes in my head.

They both have to be perfect squares to produce integer outcomes and 1 clearly doesn't work, so 9,4 is the only solution with x and y both less than 11. In fact with anything from there up to 16 on the right side of either equation you can easily prove whether the solution exists or not and it must be comprised of 9, 4 and 1. Let's say √x+y=n, x+√y=m, m,nn. With constants

"[Ramanujan solved this] somewhere at the start of the 1st century...while talking to ghosts or some shit"

I can feel the passion emanating from this man, great video :)

Great video, Papa! One thing: If we determine that the two variables x and y are natural (bc we are trying to solve a Diophantine Eq.), can't we just automatically assume that they are square numbers (

Damn I thought no more videos on indian mathematicians after the InDiAn ScEmMeR video but gg

“While talking to ghosts or someshit; I don’t remember” 😂🤣

HOW IS HIS BOARD SO CLEAN ALL THE TIME? WHAT THE HELL?

I randomly picked 9 when I saw that thumbnail and realised that it fits, lol

Add both equations and factorise the new equation as √x(√x +1) + √y(√y + 1)=18 and now put perfect squares till you get the answer. :D

Bruh I really nearly had an aneurism trying to figure out where the coefficient 2 of sqrt(x) went at 8:00

Why do the factors of 4 have to be integers. I understand integers for x and y but not the factors of 4.

@EdwinSteiner

2 жыл бұрын

The original two equations imply that if x and y are integers, then sqrt(x) and sqrt(y) must also be integers. The factors in the equation are sums/differences of these and integers, so they must also be integers.

Would this method work ? if x+sqrt(y) = 11 x = 11-sqrt(y) so you can use it above : sqrt(11-sqrt(y))+y = 7 you solve for y then get x by replacing in both originals equations

I just looked at this for like 5 seconds and it just 9 and 4 lol

When I was at high 10 years ago I had solved this question Because it was printed on the back cover of my mathematics book The way I solved this question At first /X=7-Y the power the both side to square X= Y^2 -14Y+49 Then /Y= 11-X and Y^2 = X^2 -22X+121 Then there replace the values Y^2= (Y^2-14Y+49)^2 -22(Y^2-14Y+49) +121 Now I think this equation is very simple to be solved

Tfw = (equal to) is not rigorous enough so you use "exactly equal to"

@vectorclassic6403

2 жыл бұрын

Fair enough ☠️

Instead of 7 & 11, I wonder if there is a generalised solution for any natural numbers, a & b ?

And now for a "so smart it's dumb" way. Solve for sqrt(x) and plug into the other equation to get y^2 - 14 y + sqrt(y) + 38 = 0. Since sqrt(y) is an integer, it must divide 38 by the rational roots theorem. Out of 1, 2, 19, 38, obviously only 2 works.

the way I was taught is that 3 lines are for defining stuff, and 2 lines are when stuff is equal without human interaction

These videos are so fun to watch!

YO I REMEMBER THIS PROBLEM. IT WAS GIVEN TO US ON SOME MATH OLYMPIAD I TOOK IN 2017 AND I WASN'T ABLE TO SOLVE :( ANYWAY NICE SOLUTION!! :)

Why do ( sqrt{x} - sqrt{y}) and ( sqrt{x} + sqrt{y} - 1) have to equal integers? Why can't they be two irrational numbers whose product is 4?

This is like 9th grade math class in Vietnam. Glad I passed that hell of time.

For all reals, how many solutions are there? x=11-sqrty sqrtx=sqrt[11-sqrty] = 7-y , so 0=

The x,y e N assumption seems kind of bad considering that it results in having to solve for various cases instead of generally

The man who knew infinity Shrinivas Ramanujan. He was birth in India (Bharat).

@vaibhavrajwani6623

2 жыл бұрын

Don't do this...he gets triggered..

@vectorclassic6403

2 жыл бұрын

The point is does anyone give a flying f### though???...

0:02 pov: you don't know what intro you want to make

while talking to ghosts lol

found solution by just picking numbers. much easier and faster : we see that SUM is odd number in both cases, so one of numbers should be odd and another should be even, othervise if both odd or both even numbers we will get even number sum. the next hint is numbers are "N" so even number which we are taking square root of should be even number which is dividible by 4 (dunno how to say that correct - my englsih is very bad :) ), so we should get like 4, 16, 36, 64, 100, 144...etc 16 and following by it are too large to fit into equasion cuz if we wont take square root of them they will exceed SUM, so we should out stay with (2)4 pair no matter what will we count as 4 (x or y) the equasion will give us 3(9) on another number, so soulution is 4 and 9

Me, an asian kid who learnt this when im 12 years old: *PATHETIC*

@vectorclassic6403

2 жыл бұрын

Nobody gives a f### ... pathetic

if the numbers get big enough, solving the equation wouldn't be this easy...

This system is so simple to solve since there are so few options for x and y. There is no need to overcomplicate it and I definitely wouldn't call the problem beautiful.

jezz I was so stupid that I tried calculating. But then I realised if I use logic I can find that y

so my tactic was fill in the right numbers and it worked

Looks like Papa's feeling better about Ramanujan today after all the previous trouble with annoying nationalists! :)

As soon as you said that x and y are natural numbers, it just clicked that sqrt x and sqrt y must be natural numbers, which automatically implies that x and y must be perfect squares and it kinda solved itself, but i do like your rigurous way to solve it. Today the youtube gods were kind and they randomly recommended this video. Praise the youtube gods

how did i solve that in just 15 seconds?!?

the equation in the thumbnail sure was easy

Where does it say x and y natural numbers???

Nice problems, but I would suggest in this video and also other videos of yours, state from the very beggining in what domain you are asking to solve. For example, you state in the 2:26 THAT the domain is the naturals number. Thanks a lot!

@PapaFlammy69

2 жыл бұрын

I said at the start that it's diophantine, so everything was settled

@dmtri1974

2 жыл бұрын

@@PapaFlammy69 Sometimes the accent is not so clear or the listening comprehension is not so good by some viewers (like me), so if not a big problem for you, why not to deal with this also?

I just plugged in perfect squares into x and y until all the numbers equaled each other.

by inspection x=9 y=4 then 7-rootx = [11-x]^2 test x:= 49 36 25 16 9 4 1 only 9 works

Please solve the CMI admission test for undergrad

Couldn't we use a substitution for X and y . For example let x=u^2 and y=d^2 . Solving for d gives us a quartic . Since the soloutions are elements of x:x belongs to n then all the soloutions of the quartic equation are factors of the constant e where the quartic equation is in the form of ax^4 +bx^3+cx^2 +dx+e . This gives us only one real natural Soloution . And by plugging it into our d^2 we will get X and y . Am I missing anything regarding the rigour I'm just a high school student so I don't know if I'm missing on sth?

I think you missed the most unintuitive part of this, being that x=9 comes out of any system where the RHSs differ by 4 (and you can pretty easily get y=4 from there). You could replace 11 and 7 with n and n+4 and still get the solution!

The 'wa' always gets me

I think you used the identically equal sign wrong. I thought it was only used if the expression was true regardless of the value of x and y. At least that’s what my math teacher said correct me if I’m wrong

Thanks for your efforts. can you help with the integration of [cos (Sqrt[x]) sin (Cbrt[x))] ?

Moral of the story: Think a little bit deeper for a more elegant solution

2 min solution: After factorizing we get root a + root b = 5 so just substitute dont need to do the long process

I solved it like a second grader by writing 1+6, ..., 6+1 and same for 11 and matching them.

but how can you make conclusion that square root x and square root y is integer?

@therealrealludwigvanbeethoven

2 жыл бұрын

Because we're trying to solve a Diophantine (which is clearly what Ramanujan intended), we may preliminarily assume that x, y are both elements of the set of Natural numbers (which are positive integers).

Thankyou

Can u please try to solve the problem where the irregular pentagon has sides 3 3 4 5, and then we have to find the last one? R is right angle ______________ | r / 3| /r\ /5 |/34 \ / /

People like him show how unfair life really is

@PapaFlammy69

2 жыл бұрын

what?

@ravenking2458

2 жыл бұрын

🤨huh?

@hajimeisayama9842

2 жыл бұрын

@@PapaFlammy69 i think he is mentioning about his death in early age...

3:30 square root of wha why ?

Proud of India for producing such great mathematicians # Ramanujan

@bhaskarporey3768

Жыл бұрын

What's your contribution on this ??

@aryanranjan418

Жыл бұрын

@@bhaskarporey3768 😂😂 What type of contribution are you talking about. Stupid

sah papa flammy 💯, I wrote to you on twitter about an easy solution to solving an integral on your ∫(ax²+bx+c/dx²+ex+c) dx video, which was making you do trig subs etc guess I wanted to help out my fellow m🅰them🅰tici🅰n

@PapaFlammy69

2 жыл бұрын

So, I understood that it can only be 2 possible answers for the equation (either 2 or 4) but can someone explain to me how would I solve for this if the number was bigger ? Like how would I solve for this if it was 32 = (√x-√y)(√x+√y-1) ?

Why do I instantly know they're 9 and 4

8:41 First time hearing someone saying that.

well explained 👍

@PapaFlammy69

2 жыл бұрын

thx :3

can you post here the link to where I can buy the Mandelbrot flag/curtain you have in the background ? Thanks.