@Peter The first part (“the iterations can converge or not”) is surely correct. The second part (“the Newtons iterations converges quickly in general”) is an oversimplification IMO.
close: the question author has no idea what is going on and needs some time to find a good question. Please help them by closing it until such improvements are made.
I don't know if the following holds, but:
Is it true that if $b$ is a power of $a$ mod p for all primes($b,a$ are positive integers), that is to say that the congruence $b\equiv a^{x} \pmod p$ has a solution for all primes, then there is some integer $n$ such that $b=a^{n}$?
Thanks in advance
This is a clear duplicate math.stackexchange.com/q/4363884/42969. Alternatively one can close for other reasons since the confusion is apparently based on a simple miscalculation.
This completely useless post has been undeleted. Please help to downvote and delete, as it has crazily gotten 35 upvotes just by being old. @ArcticChar @RRL @KReiser @MartinR (I and some others cannot vote again.)
I don't know if the following holds, but:
Is it true that if $b$ is a power of $a$ mod p for all primes($b,a$ are positive integers), that is to say that the congruence $b\equiv a^{x} \pmod p$ has a solution for all primes, then there is some integer $n$ such that $b=a^{n}$?
Thanks in advance
