Source: Czech-Polish-Slovak Junior Match 2024, T-5
Tags: number theory, number theory proposed, Digits, palindromes, Powers of 2
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Is there a positive integer $n$ such that when we write the decimal digits of $2^n$ in opposite order, we get another integer power of $2$?
hmm isn't that for 2^n less than 10 all work?
StarLex1 wrote:
hmm isn't that for 2^n less than 10 all work?
I guess "another" should be interpreted as "a different" here (this might be a translation issue).
https://artofproblemsolving.com/community/c6h616680p3673607 is a more general version of this problem.
The answers no by just considering mod 9, and the powers are within a range of 3 from each other