Cheenta
How 9 Cheenta students ranked in top 100 in ISI and CMI Entrances?
Learn More

Application of Cauchy's Functional Equation - INMO 2018 Problem 6

An Application of Cauchy's Functional Equation


Cauchy's functional equation is a description of a function. Lets look at Indian National Math Olympiad 2018's Problem 6 which can be solved as an application of Cauchy's Functional Equation:

$$ f(x + y) = f(x) + f(y) $$

INMO 2018 Problem 6

Let N denote the set of all natural numbers and let (f : N\rightarrow N) be a function such that
(a) (f{(mn)} = f {(m)} f{(n)}) for all m,n in N ;
(b) m+n divides (f {(m)} + f {(n)} ) for all m, n in N
Prove that there exists an odd natural number (k) such that (f {(n)} = n^k) for all n in N.

Discussion

Next

Knowledge Partner

Cheenta is a knowledge partner of Aditya Birla Education Academy
Cheenta

Cheenta Academy

Aditya Birla Education Academy

Aditya Birla Education Academy

Cheenta. Passion for Mathematics

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.
JOIN TRIAL
support@cheenta.com