MathDB

(f,p) f is function, p is polynomial

Source: Indonesia IMO 2007 TST, Stage 2, Test 4, Problem 3

November 15, 2009

functionalgebrapolynomialinductionnumber theory proposednumber theory

Problem Statement

Find all pairs of function

f: \mathbb{N} \rightarrow \mathbb{N}

and polynomial with integer coefficients

p

such that: (i) p(mn) \equal{} p(m)p(n) for all positive integers

m,n > 1

with \gcd(m,n) \equal{} 1, and (ii) \sum_{d|n}f(d) \equal{} p(n) for all positive integers

n