Power Of $2$

For discussing Olympiad Level Number Theory problems
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samiul_samin
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Power Of $2$

Unread post by samiul_samin » Tue Feb 20, 2018 4:39 pm

Does there exist a natural number $N$ which is a power of $2$ ,such that one can permutate its decimal digits to obtain a different power of $2$ ?

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samiul_samin
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Re: Power Of $2$

Unread post by samiul_samin » Tue Feb 20, 2018 4:43 pm

Hint
Think about the size of $2^k$ and $2^{k+4}$ for,$k=1,2,3,...$
Answer
NO
Problem source
17th Iranian Math Olympiad
Solution source
You can get an elegant,awesome and titanic solution of this problem in this book:
Screenshot_2018-02-20-16-35-44-1.png
(You can get the PDF easily by using internet.)

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