/sci/ - Science & Math

>>15384684
Solved it, D is the answer.
Hint for other anons - s is included in the divisor series, s is the greatest divisor of s and LCM.
Also I am an Asian.

Homework thread

>>15384708
> t. Wasn't able to solve it

That's trivial. Doesn't require any knowledge of mathematical theorems. Any highschool kid with a non-retard IQ can see it. I'm a black woman btw.

>>15384736
Yeah why don't you post your solution larping nigger?

>>15384720
Ok, well A and B are trivially false.

If we expand the sum it's equal to:
[math]\frac{x_{1}+ x_{2} +x_{3}+...}{x_{1}x_{2}x_{3}...}[/math]
[math]=\frac{2280960}{x_{1}x_{2}x_{3}...}[/math]
[math]=\frac{2280960}{s}[/math]

So D would be the answer

>>15384736
Also
> Doesn't require any knowledge of mathematical theorems
kek, at this point I am curious to know how many basedence faggots on this board can solve this.

>>15384684
D

I’m black btw

>>15384748
get your prolapsed ass out of here dumb newfag

>>15384748
>Pure math
>Science
Kys

>>15384741
Retard. Pls commit an hero or at least castrate yourself to prevent the propagation of your inferior genes, not that you could, but better safe than sorry.

Look at this >>15384770 80IQ mutt coping, thinks that shitty problem is le heckin "pure math" just cuz he can't solve it

>>15384771
> Oogga Bogga!!!
Post solution or shut up nigger

>>15384777
please specify the precise scientific discipline this problem allegedly belongs to. furthermore, specify the exact application it has, with a journal publication. otherwise, fuck off and seppuku.

i mean, just make a trivial analog. let p be prime. then s = 1 + p and 1/1 + 1/p = (p+1)/p. this argument is easily extended to composite numbers. hell you can literally prove this using induction.

>>15384789
/sci/ = science&math

>>15384793
not the argument being made, dumbass. >>15384748
>> Doesn't require any knowledge of mathematical theorems
>kek, at this point I am curious to know how many basedence faggots on this board can solve this.
obviously "basedence" was from the filter of this anon trying to say "soience" which is clearly a play on the word "science" as a pejorative. despite this being a math and science board, that doesn't mean every topic is science. if you can't understand this, then you're one of the few retards itt.

It's D
Hint is if Xi is devides s then Xm-i+1 devides it too

>>15384684
This would be an AIME quality problem without the multiple choice. With the multiple choice it's baby tier

>>15384797
I can tell by your use of profanity that you're emotionally distressed. Have we hit a soft spot, anon?

>>15384741
With barely any math you can construct a toy example with a handful of small integers and it becomes clear that the denominator is s and that 1 can't possibly be the numerator.

>>15384818
>dumbass and retard is profanity
top kek.

>>15384684
D

I'm mixed race

>>15384826
Did you receive too much love from your father?

>>15384832
do you honestly view the term "retard" as profanity? if so, you're clearly retarded.

>>15384835
I'm sorry to have hurt your feelings, but you're clearly retarded. Childhood trauma manifests differently for everyone.

>>15384748
>>15384818
The second you get any pushback you resort to calling people 'mutts' and then calling them 'mad'. Why are you here? You can just go back to /pol/ and go talk about how white men are superior with all of your other (supposedly) white friends. Why do you want to annoy people here?

If m=1, then that sum is equal to one, which appears inconsistent with the choices.

>>15384840
Nevermind, I missed the x_m on the previous line.

>>15384839
why the profanity? did your father love you too much?

>>15384847
It is obvious that you have engaged in mimicry as a subconscious form of self-defense. It's alright, anon, you're safe here.

>>15384858
you sound emotionally disturbed.

>>15384684
We basically need to prove that divisors exist in pairs
6 = 1•6 = 2•3 = 3•2 = 6•1

>>15384897
One way to approach is to take into context the fact that the divisors are clearly < s hence the quotients must also be < s
so we have x1 < x2 < x3 < .... < xm < 6
and q1 < q2 < q3 < ... < qm < 6
it follows from here that at some point the product xi•qi is basically the reverse permutation of itself that is qi•xi

>>15384897
Nice. Doing your part to spoonfeed the brainlets

>>15384939
What do you think of this >>15384937, can you help me to further elaborate this proof?

>>15384684
>white man
Kek, way to out yourself pajeet

>>15385016
explains why he got so upset when he got called out for not understanding the difference between math and science (i.e., he didn't know english).

>>15385016
I feel disgusting now that I have seen this, those options were a red flag, Jeets don't understand math on a fundamental level , for them it's all about heckin "tricks" and shieet.

>>15385045
since you know 1 is a divisor, that automatically eliminated a) and b) as answers since the sum should be 1 + ..., so the pajeets are bragging over a 50/50 guess kek

>>15385050
Yeah that's what I am saying only jeets can have these sort of problems in a multiple choice format, they don't care about Math.

>>15384684
Withtout loss of generality let
[eqn]x_1 \leq x_2 \leq \ldots \leq x_m[/eqn]
Then obviously
[math]x_k x_{m+1-k} = s[/math] for [math]k=1,2,...,m/2[/math]
So you can group the summands as pairs:
[eqn] \sum_{i=1}^{m} \frac{1}{x_i} = \sum_{i=1}^{m/2} \left( \frac{1}{x_i} + \frac{1}{x_{m+1-i}} \right) = \sum_{i=1}^{m/2} \frac{x_i + x_{m+1-i}}{s} = \frac{\sum_{i=1}^m x_i}{s} = \frac{2280960}{s}[/eqn]

>>15385118
Yeah you need to prove that "obviously" part. Here is a start >>15384937

>>15385118
>wlog
>doesn't work for primes
dummy

>>15385144
It does work nigger

>>15385144
It works for 2280959 which is the only prime with the right sum of divisors.

>>15385130
Guys, proving this shit is giving me a panic attack. I'm no mathematician so it isn't obvious to me how to do it, yet intuitively I find the conclusions to be obvious. This discrepancy in thinking is causing a lot of distress.

>>15385226
Kill yourself and stop trying to prove shit you are not a genius you are fucking worthless

>>15384684
How gay is this language, LET X BE Y , LET THIS BE THAT.

HOW ABOUT, SUCK ON MY HUGE COCK.

>>15384684
D.
I reasoned by using s = 15 and x = [1,3,5,15].
Replace 2280960 with 1+3+5+15 = 24 and you can convince yourself that D is the correct formula.

>>15385281
Your dick is 5 in max, stop lying

>>15385318
BTW I am an engineer and I reason most problems like this. Math is easy as fuck.

>>15384684
Why do mathematicians say positive integer instead of natural number

s=|int| and dividend(s)=1 x_i=2^(-1≥int n) and dividend(s)_1+dividend(s)_2+dividend(s)_3...+dividend(s)_m=m Σ(index of summation=1 and final index=m)=sm and x_1+x_2+x_3...+x_m=2280960 Σ(index of summation=1 and final index=m)=2280960(s) >>15384684=fag
Q.E.D.

>>15385366
Don't know where you heard that but it's pretty much without conventions so who knows, people just go along various notations.
For example I've seen people use [math]\Pi[/math] for primes instead of [math]\mathbb{P}[/math]

let [math]d_1, d_2, \cdots, d_n[/math] be all the divisors of [math]z \in \mathbb{N}[/math], let [math]D[/math] be a set [math]D = \{d_1, d_2, \cdots\}[/math] and let [math]S = \sum\limits_{d \in D} d[/math]
without loss of generality, let's assume [math]d_1 < d_2 < ...[/math]

let [math]\mathbb{P}[/math] be a set of all prime numbers; by the fundamental theorem of arithmetics there
always exists a unique factorization [math]s=f_1 f_2 \cdots[/math], such that [math]\forall i. f_i \in \mathbb{P}[/math]; let [math]F[/math] be a set [math]F = \{ f_1, f_2, \cdots\}[/math]

thus [math]\forall i. \exists F_0 \subseteq F. d_i=\prod\limits_{f \in F_0}f[/math] and [math]\forall i. d'_i=\prod\limits_{f \in (F \setminus F_0)}f=\frac{z}{d_i}\in D[/math] [spoiler]idk about the notation :)[/spoilder]

consider two divisors [math]d_i[/math] and [math]d_{i+1}[/math]: from [math]d_1 < d_2 < ...[/math] follows [math]d_i<d_{i+1}[/math] and thus [math]d'_i > d'_{i+1}[/math]
notice that [math]\neg \exists j. d_i < d_j < d_{i+1}[/math] and thus [math]\neg \exists j. d'_i > d'_j > d'_{i+1}[/math]; therefore, from [math]d_i=d'_j[/math] follows [math]d_{i-1}=d'_{j+1}[/math]

notice that [math]d'_1=\frac{z}{d_1}=d_n[/math]
thus, by the principle of induction, [math]\forall i. d_i = d'_{n-i+1} = \frac{z}{d_{n-i+1}}[/math] and therefore [math]\forall i. \frac{1}{d_i} = \frac{d_{n-i+1}}{z}[/math]

then [math]\sum\limits_{d \in D} \frac{1}{d}=\frac{d_n}{z}+\frac{d_{n-1}}{z}+\cdots=\frac{S}{z}[/math]

it is known that [math]S=2280690[/math], so the answer is D

>>15385912
whoops, it should be "...from [math]d'_i=d_j[/math] follows [math]d'_{i-1}=d_{i+1}[/math]"

>>15385941
/s/[math]i+1[/math]/[math]j+1[/math] >:(

>>15384684
D is the only non retarded answer. showing D is correct is not obvious but showing A-C are wrong is trivial

>>15384684
Each fraction in the summation can have common denominator of s because they are all factors. If we do this, it leads to (x1 + x2 + ... + xm)/s which as shown by the original conditions is 2280960/s so d is the right answer
>t. Hapa

>>15385979
There is an obvious way to show D is right >>15386006
The fact that they are factors means that they have a common denominator of x, and facotrs by definition multiply into eachother to make that common denominator, so you can turn the summation into (x1+x2+...+xm)/s

>>15385912
>by the principle of induction
Can you not please? Just say "by induction".

>>15384684
Let n be an integer. Observe that
1/d=d/n
for any divisor d of n.

It follows that the sum of the reciprocals 1/d of the divisors of n is equal to the sum over all fractions d/n where d is a divisor of n. This value is then equal to the sum of all divisors, divided by n. Using there notation, this is the value
(x_1 + ... + x_m)/s

We are given that sum of divisors is equal to 2280960. Substituting this into the above expression, we obtain
2280960/s.

pic unrelated

>>15386400
>Observe that
>1/d=d/n
>for any divisor d of n.
As expected, the poltard drone is retarded

>>15386400
>>15386415
>t. Mathlet retard
That was a typo, as you would have easily realized of you werent a typical self-righteous and intellectually condescending SJW type. I meant to write 1/d=(n/d)/n. This is basically mobius inversion, as anyone with a math background would know. The dividers d and n/d of an integer n are in an related by an order reversing bijective correspondence.

Pic related is a proof.

Btw
COVID came from a lab.
Epstein didnt kill himself.
You will never be a woman.

>>15386415
I typed it up in Latex, so now you have to take my word for it, since I'm an expert.

Hold on guys let a White man (myself) take a stab at this. As a White male, I say the answer is D. I'm right because I'm a White male.

1/x_{i} * s = x_{m+1-i}, that gets you the answer. I'm asian

^^ After sorting ofc

>>15386451
You will never be a mathematician

>>15384684
Are you retarded? I'm an actual mathlet whose just got to Chapter 3 in Lang Basic Math, and even I understand why D intuitively makes sense.

>>15384748
count me into the unable to group, which will be an overwhekming majority. I'm still going to make an uneducated guess that will make you faggots seethe with at how accurate it is to the actul outcome, dont ask me why 93.17% is the answer either.

>>15384684
That sum should actually be zero because for every positive divisor there is an opposite negative divisor.

>>15386601
>positive integer 's'

>>15386607
Positive numbers have negative divisors retard, or do you think (-2)(-5)≠ 10?

>>15386609
I know you may be autistic, let me lay it out for you: "positive integer" is another name for natural number, and "divisor" can mean just the positive divisors, depending on the context. Your redditor gotcha failed, kill yourself.

>>15384684
Stopped reading at divisors. I don't give a shit about number theory, if your math doesn't involve [math]\mathbb{R}[/math] then I'm not interested.
>Inb4 b-but the integers are a subset of [math]\mathbb{R}[/math]
Kill yourselves discretefags

D
I’m Italian

>>15386777
Worthless analysis college kiddy,, number theory is literally pure math, if you want to play with children toys go do engineering or something you worthless talentless non genius tranny

>>15384684
this is not a good test, because these are learned skills. chinks are better than us at these kind of tasks specifically.

>>15386618
>can mean
Doesn't necessarily mean. You're making an assumption. Based on the phrasing of ops question, negative divisors are allowed. Pick up your favorite textbook on this stuff and it would specific the xi are positive. Pajeets just don't understand how to be explicit

I got masters in math 1 year ago, I have only done ML since, so my brain is basically mush at this point.. but is this not trivial??

Just multiply with s?: s * \sum 1/xi = x1 + ... + x_m => \sum 1/x = (x1 + ... + x_m) / s?

>>15386451
>>15386474
>>15386400

>COVID schizo
>poltard
>can't do basic math
>unironically supports Russia
>Unironically using the phrase "SJW" in 2023

Can't say I'm surprised. Wtf are you even doing on sci? Why don't you go back to your containment board. I think you get a lot more feedback on you seething about muh "SJWs" and you're schizo theories about Russia and the COVID lab leak conspiracy theory.

Also this >>15386537. You're a fucking retard an you literally need to go back to middle school algebra.

>>15387229
Keep crying. You won't get that covered TT position. Then you'll be coping and wondering what use your math degree is.

D

Product of divisors is s^m/2 (pair off x and s/x)

Combine fractions in the sum to get

sum(s^m/2 / x) / s^m/2
= s^(m/2-1) * sum(s/x) / s^m/2
= s^(m/2-1) * sum(x) / s^m/2
= big number / s

>>15387229
>>Unironically using the phrase "SJW" in 2023
This. The proper modern term is "neo-bolshevik". Or just "troon"