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 $f(5)$?
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1Nice try, what have you tried? – Michael Hoppe Oct 17 '13 at 14:03
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What is $f(1)$ under these conditions? – Daniel Fischer Oct 17 '13 at 14:05
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2This 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
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I flagged it. Lets see what happens. – Marc Palm Oct 17 '13 at 15:36
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3This 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
3 Answers
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$f(2) = f(1)^2 = 9$, what is $f(5) = f(1)^{5}$ then?
Marc Palm
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1This is a live math problem on Brilliant. Please close this for a week. - Calvin Lin, Brilliant Challenge Master – Calvin Lin Oct 17 '13 at 15:06
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We have $$ f(2)=f(1)^2=9. $$ Thus $f(1)=3$ and $$ f(5)=f(1)^5=3^5=243. $$
Leox
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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 15:06
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As mentioned, this is a live math problem on Brilliant. Solutions are available. The image intentionally cuts off the first solution.
Calvin Lin
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