Difference between revisions of "2021 JMPSC Sprint Problems/Problem 15"
| Line 13: | Line 13: | ||
~Mathdreams | ~Mathdreams | ||
| + | == Solution 3 == | ||
| + | <cmath>100^{10} \equiv 0 \mod 100</cmath><cmath>5^{10} \equiv 25 \mod 100</cmath>Therefore, the answer is <math>75</math> | ||
| + | - kante314 - | ||
==See also== | ==See also== | ||
Revision as of 09:45, 12 July 2021
Problem
Find the last two digits of 
Solution
Note that 
and 
.
. 
Solution 2
By multiplying out several powers of 
, we can observe that the last 
digits are always 
(with the exception of 
where 
). Also, 
ends with several zeros, so the answer is 
.
~Mathdreams
Solution 3
![\[100^{10} \equiv 0 \mod 100\]](http://latex.artofproblemsolving.com/b/a/0/ba0ec0b3d29299e35f0ef779a6a76a64cc7f6889.png)
![\[5^{10} \equiv 25 \mod 100\]](http://latex.artofproblemsolving.com/a/5/3/a531d4ef151426b71ae88922bda2fa695d562dc6.png)
Therefore, the answer is 
- kante314 -
See also
The problems on this page are copyrighted by the Junior Mathematicians' Problem Solving Competition. 
