NUMBER THEORY Functional Equation from *Japan*!

#mathematics #olympiad #math
In preparation for last year's International Mathematical Olympiad held in Japan, we saw a beautiful number theory problem from the Japan Math Olympiad 2023. Would there be another beautiful number theory problem in this year's Japan Math Olympiad?

[@dedekindcuts3589]

Did you like this problem?

[@amaldev5970]

yeah, got to learn something new, NT FE has always been on my weaker side!
Thank you!

[@aadfg0]

Possible alternate solution: prove f(1)=1 through whatever means necessary. After that:
n = f(m), 2f(m) -> m|2f(m), 3f(m) -> m|f(m).
n = 1 -> f(m)(f(m)+1) = lcm(m, f(m+1)) ≤ mf(m+1) -> f(m)≤m. By divisibility, f(m)=m.

[@dedekindcuts3589]

Did you find an easy way to prove f(1)=1? I can't remember the details now but if I recall correctly I struggled to prove that as well. Rest of solution seems short!

[@MdRiyadBabu-uy1dl]

Nice problem of Japan that you solved

[@1468_math]

I solved the problem in under examination. It was a fun problem!

[@dedekindcuts3589]

Congrats! It is a fun problem indeed!

[@skrrrrrrrrt]

I see Anya, I click

[@Mather4269mixti]

Japan's nt always so cool