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im bored give me a number to prime factorize
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Screw factorizing specific numbers; do some introductory Analysis 1 homework:
Proof that every integer > 1 can be factored into primes, and that its unique (ignoring order)
(since its ana1 do it via induction please^^)
Its the Fundamental Theorem of Arithmetic
and yea it was 1/4th of our students homework after the second lecture in Ana1 while I was tutor (or a variation of it -> e.g. all even numbers, just so they cant google it... AI probs makes those efforts useless though)
its great for understanding how induction proofs work, but also then having them think about the problem after the induction (since that doesnt prove the order yet)
(that being said I wouldnt call it easy for Ana1 students at that point, cause those homework sheets were rough to grade)
at least I understand #2 and #4 but why r some of yall giving me a number that’s already a prime number
BerLINglazer, if you see this, ik you dont do much with the time you have, please sign into a chess club, you are really talented
https://www.chess.com/game/live/172694907848?username=rubymeow7
i did and this is how it went
u lucky he ran out of time, and also, im nobody to tell you this, but why dont you trade pieces, im only 1k elo and i trade pieces anytime in this game (the prolly wouldnt have come to a stage where pieces are tradeable anyways if i was playing)
on 14th move i didnt trade cuz i rly didnt want to relinquish my bishop pair, 16th move i traded cuz i could win a pawn
18th move i played b5 but honestly i probably shouldnt have done that, my e4 pawn and the knight on the c3 were already unstable and having the lone pawn on b5 kinda made it vulnerable to future overload tactics
on 21st move i didnt want their bishop to take my knight cuz them my e4 pawns gonna be unprotected
25th move i probably shouldve traded my rook cuz rxc8 bxc8 and nd4 looks pretty hard to defend
a lot of them have been troll but here’s two fun ones, it’s not the greatest to bash but if you can figure something out then it gets easier
8365427
40081
first one i have no idea
2nd one looks like theres smth cuz its [(200)^2]+[(9)^2] but idk how to make progress from here
the first one is (200 + 3)^3, you can see the binomial expansion if you look closer (8000000 + 360000 + 5400 + 27), so it factors into 203^3
the second one is called sophie germain factoring, if you have x^4 + 4y^4 you can factor it as (x^2 + 2xy + 2y^2)(x^2 - 2xy + 2y^2), so since 40081 is 3^4 + 4*10^4 you can plug in to get 149 x 269
I have forgotten Binomial expansion, but definitely learnt something new in the 2nd one. W nataliee!
lowkey i might just start posting fun math problems every day for vlr, i have a ton i can post
lol, ok, I'll read some. Don't think it'll get much attention though. Aren't most of them lengthy?
nah most of them are pretty chill tbh
like for example the area of a given circle is log₁₀([100!]²). find the radius of the circle to the nearest tenth
bru there’s no way i would get that ur like infinite times smarter than me
you are 2000 in chess, i didn’t know your mathematical ability so i tried to guess your level
the only germain I know was PSG XD.
I don't think this factorization is taught though, wasn't taught in India
AM GM is taught in schools no? that’s just a basic geometric proof that takes like 10 minutes lol
most students can state the inequality just fine but can't use it to solve problems. most factorization tricks are also introduced to kids through problems that the students never get to go over except u frequent aops or something
ahh fair enough, i go to aops just to look at past amc12/aime problems but i dont chat there or anything
does bro know Euler's tortient function, Fermats Little theorem, and modular arithmetic tho
ive touched on modular arithmetic but im a lazy student so i havent really gone beyond my exams
it’s not standard school curriculum lmao i’m an AIME qualifier and i study competitive math so i know a lot of math way outside of the typical line of study :3
23!. very easy but don't write everything out by hand, that'll take hours
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