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2021 JMPSC Sprint Problems/Problem 15

Revision as of 09:01, 11 July 2021 by Megarnie (talk | contribs) (→‎Solution)

Problem

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

Solution

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

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

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