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).

Solution

See also

2016 UNM-PNM Contest II (ProblemsAnswer KeyResources)
Preceded by
Problem 6
Followed by
Problem 8
1 2 3 4 5 6 7 8 9 10
All UNM-PNM Problems and Solutions

[[Category:]]