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Find all solution of function

Source: Moldova JBMO TST 2005 day 1 problem 4

August 15, 2014

functionmodular arithmeticinductionalgebra unsolvedalgebra

Problem Statement

Let the

A

be the set of all nonenagative integers. It is given function such that

f:\mathbb{A}\rightarrow\mathbb{A}

with

f(1) = 1

and for every element

n

od set

A

following holds: 1)

3 f(n) \cdot f(2n+1) = f(2n) \cdot (1+3 \cdot f(n))

; 2)

f(2n) < 6f(n)

, Find all solutions of

f(k)+f(l) = 293

k<l