csat-suneung 2014 Q14

csat-suneung · South-Korea · csat__math-A Permutations & Arrangements Counting Functions with Constraints

For a natural number $n$, $f ( n )$ is defined as follows:
$$f ( n ) = \begin{cases} \log _ { 3 } n & ( n \text{ is odd} ) \\ \log _ { 2 } n & ( n \text{ is even} ) \end{cases}$$
For two natural numbers $m , n$ with $m, n \leq 20$, how many ordered pairs $( m , n )$ satisfy $f ( m n ) = f ( m ) + f ( n )$?
(1) 220
(2) 230
(3) 240
(4) 250
(5) 260

For a natural number $n$, $f ( n )$ is defined as follows:

$$f ( n ) = \begin{cases} \log _ { 3 } n & ( n \text{ is odd} ) \\ \log _ { 2 } n & ( n \text{ is even} ) \end{cases}$$

For two natural numbers $m , n$ with $m, n \leq 20$, how many ordered pairs $( m , n )$ satisfy $f ( m n ) = f ( m ) + f ( n )$?\\
(1) 220\\
(2) 230\\
(3) 240\\
(4) 250\\
(5) 260

Paper Questions

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