# $f(x+y)=f(x)f(y)$ [closed]

Let $f$ be a function from the positive integers to the positive integers that satisfies the property: $$f(x+y)=f(x)f(y)$$ for all pairs of positive integers $(x,y)$.

If we are given that $f(2)=9$, what is the value of $f(5)$?

• Nice try, what have you tried? – Michael Hoppe Oct 17 '13 at 14:03
• What is $f(1)$ under these conditions? – Daniel Fischer Oct 17 '13 at 14:05
• This is a live math problem on Brilliant. Please close this for a week. - Calvin Lin, Brilliant Challenge Master – Calvin Lin Oct 17 '13 at 15:04
• I flagged it. Lets see what happens. – Marc Palm Oct 17 '13 at 15:36
• This question is a question on an open contest and the contest organisation has requested that it be closed until the contest finishes. – Peter Taylor Oct 17 '13 at 16:12

$f(2) = f(1)^2 = 9$, what is $f(5) = f(1)^{5}$ then?
We have $$f(2)=f(1)^2=9.$$ Thus $f(1)=3$ and $$f(5)=f(1)^5=3^5=243.$$