Pretty Chill.
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- Опубліковано 4 гру 2023
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Today a super chill diophantine system of equations. Enjoy! =D
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About your method of solving 41 = (a+b)(a-b). Should you not consider 41 = -1*-41, so a+b = -41 and a-b = -1. I'm guessing you get the same answers but with a = -21 which doesn't matter for n. But in general is this not important to consider, or is there some symmetry or something that lets you skip it?
Oh yeah, you are right! Seems like I didn't notice this branch of solutions this time around, thank you for mentioning it!!!
Exactly, cause if you linearise the quadratic only the one way you don't end up with +- in front of a, just in front of b. So all solutions were found except for a = -21.
I solved this by noticing that the equations resembles the expression for a difference of consecutive squares as 20 and 21 differ by 1
(x+1)^2 - x^2 = 2x + 1
using a^2 - b^2 = 41 you get a = x + 1, b = x, x = 20
using the first equation: n + 20 = 441 so n = 421
it's chill systems like these one can relax to... all cases lead to the same result as if no worry in the world, no stress of making wrong choices or missing a case... chiiilllll
Anything that is math related is most stressing, frustrating and chill thing to do! Haha. Cheers for your work
skill issue
I got the answer by noticing that n is in between two squares given that it's plus 20 for a^2 and minus 21 for b^2.
So observing the pattern between squares we get that 2k+1, where k is the number before the next square making 2k+1 how far away the next square is.
Since n is between two squares, that means the difference between those two squares is 41.
setting 2k+1 = 41, we get k = 20.
This is the value of b, making a equal to 21. And this makes n equal to 421.
n = 421, a = 21, b = 20.
42 Hitchhikers guide to the galaxy reference, nicely done. I took a sudefed so the brain is already fuzzy. I have no earthly idea what you go on about, but for therapy, can't be beat, thank you.
Love the videos man, just found your channel again. I remember some time ago you stopped posting, so glad your back, love the maths you do! Love from England.
I solved it by noticing your dank tendencies reducing the problem down to 69, 420 and 1337. From there it was easy trial and error
:'D
I got n = 421
I saw the thumbnail and thought if I could do it by myself
I basically solved for n in terms of b and then found an equation for a^2 -b^2 = 41
Since a^2 - b^2 can become (a+b) (a-b), and 41 is prime, one of them has to be 1 and the other 41, so a+b = 41, a-b = 1, so it’s 21 for a and 20 for b, then solve for n
Let’s see if I was right gonna watch now
I was going to consider the other case but realized it was symmetrical, such that when you square the numbers it’s the same so I didn’t bother so that’s what happened but it is more mathematically rigorous to consider both cases
Yay! I was right.
Nice! =D
Technically, there are 4 solutions, as both a and b can be positive or negative.
I do not want to accept 41 is prime, this doesnt feel right
41=(5+4i)(5-4i)
nice gaussian integer
Proof by denial
Oh man. Wait till you find out 67 is prime. Or 103. And don't even think about 149.
@@STEVE_K_J not 149! (
If u had just swapped the plus and minus in the original system of equations you would've gotten n=420 as an answer😭😭
Nice and chilling
Chill
Nice promblem
Fact
Megachill, dude
succ(420)
Nobody's judging you here
42 is THE Prime Number.
Nice, something to watch while trying to get an old hentai game running
Ive never played any, do recommend
Why is 420 funny?
en.m.wikipedia.org/wiki/420_(cannabis_culture)
Neat
Do you play chess
I got 421. Not 420 :(
It is 421 !
@PapaFlammy69 yeah, but the answer isn't 420! It's so darn close!
Once again I turned off Adblock for this video.