4

Part of 2005 Junior Balkan Team Selection Tests - Moldova

Problems(1)

Find all solution of function

Source: Moldova JBMO TST 2005 day 1 problem 4

A

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

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

f(1) = 1

and for every element

n

A

following holds: 1)

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

f(2n) < 6f(n)

, Find all solutions of

f(k)+f(l) = 293

k<l

functionmodular arithmeticinductionalgebra unsolvedalgebra