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

Lifting the Exponent

Revision as of 18:21, 11 January 2024 by Wescarroll (talk | contribs) (Created page with "Let <math>p</math> be an odd prime, and let <math>a</math> and <math>b</math> be integers relatively prime to <math>p</math> such that <math>p \mid (a-b)</math>. Let <math>n</...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Let $p$ be an odd prime, and let $a$ and $b$ be integers relatively prime to $p$ such that $p \mid (a-b)$. Let $n$ be a positive integer. Then the number of factors of $p$ that divide $a^n - b^n$ is equal to the number of factors of $p$ that divide $a-b$ plus the number of factors of $p$ that divide $n$.

Retrieved from "https://wiki.aopstest.com/wiki/index.php?title=Lifting_the_Exponent&oldid=210486"