MathDB

3

Part of 2023 India Regional Mathematical Olympiad

Problems(2)

RMO 2023 P3

Source:

10/29/2023
For any natural number nn, expressed in base 10 , let s(n)s(n) denote the sum of all its digits. Find all natural numbers mm and nn such that m<nm<n and (s(n))2=m and (s(m))2=n. (s(n))^2=m \text { and }(s(m))^2=n .
number theory
RMO KV region P-3

Source:

10/29/2023
Let f(x)f(x) be a polynomial with real coefficients of degree 2. Suppose that for some pairwise distinct real numbers , a,b,ca,b,c we have:\\
f(a)=bc,f(b)=ac,f(c)=abf(a)=bc , f(b)=ac, f(c)=ab Dertermine f(a+b+c)f(a+b+c) in terms of a,b,ca,b,c.
algebraPolynomialspolynomial