Art of Problem Solving
Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Mock AIME 1 2005-2006/Problem 7: Difference between revisions

← Older editNewer edit →
Aimesolver (talk | contribs)
122 edits
Line 6: Line 6:
== Solution ==
== Solution ==


<math>2006</math> = <math>2*17*59</math>, so <math>f(2006^{6002})</math> has <math>6003^3</math> positive divisors. <math>6003</math> = <math>(3^2)(667)</math> so <math>6003^3</math> has <math>(6+1)(2+1)</math>, or <math>\boxed {021}</math> divisors.
<math>2006</math> = <math>2*17*59</math>, so <math>f(2006^{6002})</math> has <math>6003^3</math> positive divisors. <math>6003</math> = <math>(3^2)(667)</math> so <math>6003^3</math> has <math>(1+1)(2+1)</math>, or <math>\boxed {006}</math> divisors.

Revision as of 05:48, 28 August 2013

Problem

Let $f(n)$ denote the number of divisors of a positive integer $n$. Evaluate $f(f(2006^{6002}))$.

Solution

$2006$ = $2*17*59$, so $f(2006^{6002})$ has $6003^3$ positive divisors. $6003$ = $(3^2)(667)$ so $6003^3$ has $(1+1)(2+1)$, or $\boxed {006}$ divisors.

Retrieved from "https://wiki.aopstest.com/wiki/index.php?title=Mock_AIME_1_2005-2006/Problem_7&oldid=56995"