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Jun 2, 2019 at 14:05 comment added GH from MO I only considered the second orange box in your post, because this was introduced by "so my question is". Please only ask one question in each MO post. That is, open a new MO post for this other question.
Jun 2, 2019 at 7:47 comment added apple Thank you for your answer. However,if M is not a prime number, will there exist a positive irrational number $\alpha$ such that $gcd(\lfloor \alpha \cdot k^n \rfloor , M)=1$ for every positive integer $n$ ?
Jun 1, 2019 at 17:38 vote accept apple
Jun 1, 2019 at 16:48 history answered GH from MO CC BY-SA 4.0