Got 5/7

[empty crest]

i only got c=1 according to gpt thats a solid 5/7
if your'e wondering this is the imo 2024/p6 the toughest of the contest, solved it in 25mins, currently in high school sophomore year

[brave drift]

its not c=1

whyd you post this in math help tho

[stark knoll]

it is the f(r)+f(-r) = 0

[brave drift]

its c=2

[stark knoll]

what could be the answeres

[brave drift]

huh

[stark knoll]

well if you solved it you probably know what are the types of the functions

so you can plug some vals and know the answers

I will give you an example f(x) = x works here

so 0 is one of the solutions for 100% so c>=1

[brave drift]

busy right now

this video is nice

https://www.youtube.com/watch?v=7h3gJfWnDoc

its a pretty tough func equation

[stark knoll]

I cannot watch it I am still solving it

[brave drift]

oh

go ob

go on

[empty crest]

yeah i got c=1 by f(r)+f(-r)=0 asw

[brave drift]

its 2

[brave drift]

btw f(r)+f(-r)=0 for all r isnt true

for every aquaesulian

so c=1 would only owrk if every aquaesulian function always satisfied f(r)+f(-r)=0, but there are aquaesulian functions where the sum takes 2 different values

for example

f(q)=2floor(q)-q (q ∈ ℚ)

for this aquae f, {f(r)+f(-r):r ∈ ℚ} ⊇ {0,-2}

aka 2 distinct vals

[half crater]

I also got f(x)=x even tho ik it's wrong

[brave drift]

pretty tough functional equation problem

f(S(r))=S(r) for all r

and for all r, f(f(r))=r+S(r)