2016 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 7

Problem

For a positive integer $n$ let $S(n)$ denote the function which assigns the sum of all divisors of $n$ . Show that if $m$ and $n$ are relatively prime positive integers then $S(mn) = S(m) S(n)$ . For example, $S(6) = 1+2+3+6 = 12$ , $S(2) = 1+2 = 3$ and $S(3) = 1+3 = 4$ , so $S(6) = S(2) S(3)$ , noting that $2$ and $3$ are relatively prime integers (they have no common divisor).

2016 UNM-PNM Contest II (Problems • Answer Key • Resources)
Preceded by Problem 6	Followed by Problem 8
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10
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2016 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 7

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