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Suppose that $m$ and $n$ are positive integers such that every prime number which divides $n$ also divides $m$ (e.g. $n=25$ and $m=10$). How do you call such numbers? having the same "prime base" ? Thanks!

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    $\begingroup$ m= 10 and n= 25 are NOT an example of "every prime number that divides m also divides n". The prime number "2" divides 10 but does not divide 25. $\endgroup$ – user247327 Mar 11 at 14:00
  • $\begingroup$ I thinks it was ok...any way, thanks for the comment @user247327. $\endgroup$ – boaz Mar 11 at 14:02
  • $\begingroup$ does every prime number that divides m also have to divide n? If not then m is just a multiple of n. $\endgroup$ – cand Mar 11 at 14:18
  • $\begingroup$ no, i mean that $m$ satysfies the following condition : $p\mid n\to p\mid m$ $\endgroup$ – boaz Mar 11 at 14:26
  • $\begingroup$ It seems cand has the right terminology $\endgroup$ – Mikael Jensen Mar 11 at 14:56

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