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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
706,934,233,012,371,600
Ansh_
01/29/2022 11:44:38
UwU
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
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Ansh_
01/29/2022 11:45:19
then it's just a cauchy functional equation lol and you can easy solve this
0
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
837,652,910,794,866,700
謝墨離
01/29/2022 11:46:45
$f(f(y))=y$ $f(f(f(y)))=f(y)$
1
0
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null
205,739
help-1
8b5ec3b18a3c480a8f91e9fb404c1816
510,789,298,321,096,700
TeXit
01/29/2022 11:46:48
**謝墨離**
https://cdn.discordapp.c…910794866708.png
837652910794866708.png
0
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
706,934,233,012,371,600
Ansh_
01/29/2022 11:46:58
wow (@_@;) scary
0
1
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
706,934,233,012,371,600
Ansh_
01/29/2022 11:47:05
heck is that
0
1
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
321,445,119,171,756,000
Shuri2060
01/29/2022 11:47:37
Aren't we done at this point
0
1
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
321,445,119,171,756,000
Shuri2060
01/29/2022 11:47:38
f is linear
0
1
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205,739
help-1
8b5ec3b18a3c480a8f91e9fb404c1816
321,445,119,171,756,000
Shuri2060
01/29/2022 11:47:41
let f = ax
0
1
null
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null
null
205,739
help-1
8b5ec3b18a3c480a8f91e9fb404c1816
321,445,119,171,756,000
Shuri2060
01/29/2022 11:47:49
or am i dumb
0
1
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
706,934,233,012,371,600
Ansh_
01/29/2022 11:48:15
👀
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
321,445,119,171,756,000
Shuri2060
01/29/2022 11:48:16
let f(ax + by) = cx + dy
0
1
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205,739
help-1
8b5ec3b18a3c480a8f91e9fb404c1816
321,445,119,171,756,000
Shuri2060
01/29/2022 11:48:26
idk.
0
1
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
837,652,910,794,866,700
謝墨離
01/29/2022 11:48:44
https://cdn.discordapp.c…43432/image0.jpg
image0.jpg
1
0
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
837,652,910,794,866,700
謝墨離
01/29/2022 11:48:46
Why I got this
1
0
null
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
706,934,233,012,371,600
Ansh_
01/29/2022 11:48:58
Scary
0
1
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
706,934,233,012,371,600
Ansh_
01/29/2022 11:48:59
Lol
0
1
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kirby your mom
8749
kirby your mom
false
205,739
help-1
8b5ec3b18a3c480a8f91e9fb404c1816
321,445,119,171,756,000
Shuri2060
01/29/2022 11:49:06
i think
0
1
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
321,445,119,171,756,000
Shuri2060
01/29/2022 11:49:12
u should write $$f^2:=ff$$
0
1
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205,739
help-1
8b5ec3b18a3c480a8f91e9fb404c1816
510,789,298,321,096,700
TeXit
01/29/2022 11:49:15
**Shuri2060**
https://cdn.discordapp.c…119171756033.png
321445119171756033.png
0
1
null
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null
205,739
help-1
8b5ec3b18a3c480a8f91e9fb404c1816
706,934,233,012,371,600
Ansh_
01/29/2022 11:49:18
that's cause you plugged 1 extra "f" inside the f(x^2 + fff(y))
0
1
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205,739
help-1
8b5ec3b18a3c480a8f91e9fb404c1816
706,934,233,012,371,600
Ansh_
01/29/2022 11:49:55
It should just be f(x^2 + y) = f(x^2) + f(y) lol
0
1
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
837,652,910,794,866,700
謝墨離
01/29/2022 11:51:36
Why
1
0
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
837,652,910,794,866,700
謝墨離
01/29/2022 11:51:42
:flonshed:
1
0
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
706,934,233,012,371,600
Ansh_
01/29/2022 11:51:44
"however, there can exist..."
https://cdn.discordapp.c…4370/unknown.png
unknown.png
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
706,934,233,012,371,600
Ansh_
01/29/2022 11:52:07
We're trying to build up in a way so we can show f(x) = cx is the only solution (@_@;)
0
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謝墨離
01/29/2022 11:52:16
Oh
1
0
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8b5ec3b18a3c480a8f91e9fb404c1816
837,652,910,794,866,700
謝墨離
01/29/2022 11:52:20
I know it now
1
0
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
837,652,910,794,866,700
謝墨離
01/29/2022 11:52:25
:hmmCat:
1
0
921,607,226,098,090,100
wiwiwi
1040
wiwiwi
false
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
321,445,119,171,756,000
Shuri2060
01/29/2022 11:52:32
oh.
0
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
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Ansh_
01/29/2022 11:52:34
Cauchy ... thing only works as long as we had the f: Q -> Q
0
1
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
321,445,119,171,756,000
Shuri2060
01/29/2022 11:52:45
Damn I wanna hear an example
0
1
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
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Ansh_
01/29/2022 11:52:47
Well, it shouldn't be that tough tbh tho
0
1
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
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Shuri2060
01/29/2022 11:52:47
of a non-linear
0
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Shuri2060
01/29/2022 11:52:52
I'm guessing its like
0
1
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
321,445,119,171,756,000
Shuri2060
01/29/2022 11:52:56
uh
0
1
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kirby your mom
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kirby your mom
false
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help-1
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321,445,119,171,756,000
Shuri2060
01/29/2022 11:52:58
Its like yeah
0
1
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
321,445,119,171,756,000
Shuri2060
01/29/2022 11:53:02
modulo arithmetic
0
1
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
321,445,119,171,756,000
Shuri2060
01/29/2022 11:53:06
mod Q
0
1
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
321,445,119,171,756,000
Shuri2060
01/29/2022 11:53:26
you can have it linear within the set $\sqrt 2 + \bQ$
0
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
510,789,298,321,096,700
TeXit
01/29/2022 11:53:39
**Shuri2060**
https://cdn.discordapp.c…119171756033.png
321445119171756033.png
0
1
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
321,445,119,171,756,000
Shuri2060
01/29/2022 11:53:40
if that makes sense
0
1
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謝墨離
01/29/2022 11:55:23
Actually
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321,445,119,171,756,000
Shuri2060
01/29/2022 11:55:27
no nvm im talking rubbish but like that vague kinda idea
0
1
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help-1
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837,652,910,794,866,700
謝墨離
01/29/2022 11:55:28
The answer is linear
1
0
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
321,445,119,171,756,000
Shuri2060
01/29/2022 11:55:38
Yes, but you have to show it.
0
1
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
837,652,910,794,866,700
謝墨離
01/29/2022 11:55:42
Yes
1
0
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
837,652,910,794,866,700
謝墨離
01/29/2022 11:55:45
:angerysad:
1
0
null
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
706,934,233,012,371,600
Ansh_
01/29/2022 11:56:13
We both and all know that > 90% functional equation solutions have f(x) = cx lol
0
1
null
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
837,652,910,794,866,700
謝墨離
01/29/2022 11:56:28
Should we just prove it it is possible in integers first
1
0
null
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null
null
null
205,739
help-1
8b5ec3b18a3c480a8f91e9fb404c1816
706,934,233,012,371,600
Ansh_
01/29/2022 11:56:34
We're trying to show it's a unique solution here 😂
0
1
null
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205,739
help-1
8b5ec3b18a3c480a8f91e9fb404c1816
837,652,910,794,866,700
謝墨離
01/29/2022 11:56:39
And prove it is rational later
1
0
null
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null
null
null
205,739
help-1
8b5ec3b18a3c480a8f91e9fb404c1816
837,652,910,794,866,700
謝墨離
01/29/2022 11:57:06
There are two answers?
1
0
null
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null
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205,739
help-1
8b5ec3b18a3c480a8f91e9fb404c1816
837,652,910,794,866,700
謝墨離
01/29/2022 11:57:16
:thinkies:
1
0
null
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
706,934,233,012,371,600
Ansh_
01/29/2022 11:57:25
Yeah f(x) = + and - x
0
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謝墨離
01/29/2022 11:57:33
:flonshed:
1
0
null
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null
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
706,934,233,012,371,600
Ansh_
01/29/2022 12:03:54
Btw.. you can also do one thing :P
0
1
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8b5ec3b18a3c480a8f91e9fb404c1816
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Ansh_
01/29/2022 12:04:20
It's a cheat way out tbh... but there'd still be things you'd have to justify
0
1
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
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謝墨離
01/29/2022 12:05:19
I love cheating
1
0
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wiwiwi
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false
205,739
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8b5ec3b18a3c480a8f91e9fb404c1816
837,652,910,794,866,700
謝墨離
01/29/2022 12:05:24
:catthumbsup:
1
0
null
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
706,934,233,012,371,600
Ansh_
01/29/2022 12:06:01
$\forall x>0, \, f(x^2) = xf(x) = \lim_{n \to \infty} (x\cdot x^{1/2} \cdot x^{1/2^2} \ldots x^{1/2^n}) f(x^{2^{-n-1}})$
0
1
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
510,789,298,321,096,700
TeXit
01/29/2022 12:06:35
**Ansh**
https://cdn.discordapp.c…233012371577.png
706934233012371577.png
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wiwiwi
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false
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8b5ec3b18a3c480a8f91e9fb404c1816
837,652,910,794,866,700
謝墨離
01/29/2022 12:06:45
:flonshed:
1
0
null
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null
null
null
205,739
help-1
8b5ec3b18a3c480a8f91e9fb404c1816
837,652,910,794,866,700
謝墨離
01/29/2022 12:07:02
If I use this in my teachers class, he’s going to beat me
1
0
null
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null
null
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205,739
help-1
8b5ec3b18a3c480a8f91e9fb404c1816
321,445,119,171,756,000
Shuri2060
01/29/2022 12:07:07
Suppose f ugly. Then this question wouldn't be given #
0
1
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205,739
help-1
8b5ec3b18a3c480a8f91e9fb404c1816
706,934,233,012,371,600
Ansh_
01/29/2022 12:07:20
:KEK:
0
1
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
837,652,910,794,866,700
謝墨離
01/29/2022 12:11:37
Is it able to prove f(1)=1
1
0
null
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null
null
205,739
help-1
8b5ec3b18a3c480a8f91e9fb404c1816
321,445,119,171,756,000
Shuri2060
01/29/2022 12:14:13
,w f(x^2+f(y))=y+xf(x)
0
1
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वाह्य
6586
वाह्य
false
205,739
help-1
8b5ec3b18a3c480a8f91e9fb404c1816
510,789,298,321,096,700
TeXit
01/29/2022 12:14:20
Results provided by WolframAlpha
0
1
420,244,167,726,333,950
kirby your mom
8749
kirby your mom
false
205,739
help-1
8b5ec3b18a3c480a8f91e9fb404c1816
321,445,119,171,756,000
Shuri2060
01/29/2022 12:14:26
qed
0
1
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null
null
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205,739
help-1
8b5ec3b18a3c480a8f91e9fb404c1816
706,934,233,012,371,600
Ansh_
01/29/2022 12:14:29
mfao
0
1
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null
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null
205,739
help-1
8b5ec3b18a3c480a8f91e9fb404c1816
321,445,119,171,756,000
Shuri2060
01/29/2022 12:14:40
srsly.
0
1
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
706,934,233,012,371,600
Ansh_
01/29/2022 12:14:52
Shuri.. explain what's wrong with
0
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वाह्य
6586
वाह्य
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8b5ec3b18a3c480a8f91e9fb404c1816
837,652,910,794,866,700
謝墨離
01/29/2022 12:14:54
Huh
1
0
420,244,167,726,333,950
kirby your mom
8749
kirby your mom
false
205,739
help-1
8b5ec3b18a3c480a8f91e9fb404c1816
321,445,119,171,756,000
Shuri2060
01/29/2022 12:14:56
with
0
1
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8b5ec3b18a3c480a8f91e9fb404c1816
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Ansh_
01/29/2022 12:15:01
$\forall x>0, , f(x^2) = xf(x) = \lim_{n \to \infty} (x\cdot x^{1/2} \cdot x^{1/2^2} \ldots x^{1/2^n}) f(x^{2^{-n-1}})$
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wiwiwi
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
837,652,910,794,866,700
謝墨離
01/29/2022 12:15:01
What happened
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8b5ec3b18a3c480a8f91e9fb404c1816
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TeXit
01/29/2022 12:15:03
**Ansh**
https://cdn.discordapp.c…233012371577.png
706934233012371577.png
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Ansh_
01/29/2022 12:15:04
doing this :notthis:
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謝墨離
01/29/2022 12:15:25
I don’t want to use things over my knowledge
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help-1
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Shuri2060
01/29/2022 12:15:33
idk really
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kirby your mom
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help-1
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謝墨離
01/29/2022 12:15:33
My teacher said it’s possible
1
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
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Ansh_
01/29/2022 12:15:37
Yes it is
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Shuri2060
01/29/2022 12:15:37
like ima asdiosdaiosdaioj
0
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
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謝墨離
01/29/2022 12:15:37
To use these things
1
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
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Ansh_
01/29/2022 12:15:40
I know
0
1
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
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Ansh_
01/29/2022 12:16:06
I'll find a way lol. I'm just being distracted like heeeeeelllll now :KEK: :QED: lmao
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help-1
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Shuri2060
01/29/2022 12:16:16
Have you shown your latest working to your teacher
0
1
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
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Ansh_
01/29/2022 12:16:21
If not ... AOPS 💀
0
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
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Shuri2060
01/29/2022 12:16:22
f(x+y) = f(x) + f(y)
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वाह्य
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वाह्य
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help-1
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Shuri2060
01/29/2022 12:16:44
and apparently we can show that it MUST be of a linear form?
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help-1
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Shuri2060
01/29/2022 12:16:47
$$f(x^2+f(y))=y+xf(x)$$
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वाह्य
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वाह्य
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help-1
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TeXit
01/29/2022 12:16:49
**Shuri2060**
https://cdn.discordapp.c…119171756033.png
321445119171756033.png
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
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Shuri2060
01/29/2022 12:16:51
Like just think for 2 secs
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help-1
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Shuri2060
01/29/2022 12:17:08
Are we sure this condition on f will 100% determine where f(pi) will be beyond a doubt
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वाह्य
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वाह्य
false
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help-1
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Ansh_
01/29/2022 12:17:10
If f can be shown monotonic :O
0
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
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Shuri2060
01/29/2022 12:17:33
no idea.
0
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
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Shuri2060
01/29/2022 12:18:05
What useful stuff have we got right now
0
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
321,445,119,171,756,000
Shuri2060
01/29/2022 12:18:20
======= -f(x) = f(-x) ff(x) = x f(x+y) = f(x)+f(y)
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वाह्य
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वाह्य
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help-1
8b5ec3b18a3c480a8f91e9fb404c1816
321,445,119,171,756,000
Shuri2060
01/29/2022 12:18:23
=======
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null