Difference between revisions of "2021 JMPSC Sprint Problems/Problem 15"

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==Solution==
 
==Solution==
asdf
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Note that <math>10^{10}\equiv0\pmod{100}</math> and <math>5^{10}\equiv25\pmod{100}</math>.
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<math>0-25=-25</math>. <math>-25\equiv\boxed{75}\pmod{100}</math>

Revision as of 09:01, 11 July 2021

Problem

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

Solution

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

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