Prove that there exists a power of three that ends with 001

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Copyright © 1996-2018 Alexander Bogomolny
Prove that there exists a power of three that ends with 001

As in a related problem, let 3^{n} and 3^{m} ^{n} - 3^{m} = 3^{m}(3^{n-m} - 1)^{m} have no common factors, 1000 is bound to divide the second factor ^{n-m} - 1).^{n-m} ends with 001!

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Copyright © 1996-2018 Alexander Bogomolny