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

Euler's Totient Theorem Problem 1 Solution

Revision as of 13:23, 23 April 2021 by Borealbear (talk | contribs) (Created page with "==Problem== (BorealBear) Find the last two digits of <math> 7^{81}-3^{81} </math>. ==Solution== This is a direct application of Euler's Totient Theorem. Since <math> \phi(10...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem

(BorealBear) Find the last two digits of $7^{81}-3^{81}$.

Solution

This is a direct application of Euler's Totient Theorem. Since $\phi(100)=40$, this reduces to $7^1-3^1\equiv \boxed{04}\pmod{100}$.

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=Euler%27s_Totient_Theorem_Problem_1_Solution&oldid=152515"