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exists a power of a whose last n digits are 0...01

Source: 2013 Saudi Arabia Pre-TST 2.3

September 13, 2020
number theoryPowerlast digits

Problem Statement

The positive integer aa is relatively prime with 1010. Prove that for any positive integer nn, there exists a power of aa whose last nn digits are 0...0⏟n-11\underbrace{0...0}_\text{n-1}1.
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