csat-suneung 2023 Q13

csat-suneung · South-Korea · csat__math 4 marks Indices and Surds Number-Theoretic Reasoning with Indices

For a natural number $m$ ($m \geq 2$), let $f ( m )$ be the number of natural numbers $n \geq 2$ such that an integer exists among the $n$-th roots of $m ^ { 12 }$. What is the value of $\sum _ { m = 2 } ^ { 9 } f ( m )$? [4 points]
(1) 37
(2) 42
(3) 47
(4) 52
(5) 57

For a natural number $m$ ($m \geq 2$), let $f ( m )$ be the number of natural numbers $n \geq 2$ such that an integer exists among the $n$-th roots of $m ^ { 12 }$. What is the value of $\sum _ { m = 2 } ^ { 9 } f ( m )$? [4 points]\\
(1) 37\\
(2) 42\\
(3) 47\\
(4) 52\\
(5) 57

Paper Questions

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