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

2021 JMPSC Sprint Problems/Problem 15

Problem

Find the last two digits of $10^{10}-5^{10}.$

Solution

Note that $10^{10}\equiv0\pmod{100}$ and $5^{10}\equiv25\pmod{100}$.

$0-25=-25$. $-25\equiv\boxed{75}\pmod{100}$

Retrieved from "https://wiki.aopstest.com/wiki/index.php?title=2021_JMPSC_Sprint_Problems/Problem_15&oldid=157834"