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Nov 30, 2015 at 22:36 comment added Brando Unfortunately, this argument seems to break down when there are three primes $p,q,r$. What could happen that $n_p=n_q<n_r$. Then if $(n_r|p)=-1$ and $(n_r|q)=1$ I don't see the same trick working.
Nov 30, 2015 at 3:28 comment added Brando No, I am thinking that $p$ and $q$ are very near in size, which prohibits this obstruction.
Nov 30, 2015 at 3:26 comment added Lucia The only fly in the ointment is if $n_p=q$ or $n_q=p$. But the OP is perhaps not interested in these pathological cases.
Nov 30, 2015 at 3:25 comment added Brando Aha I suspected it should be simple!
Nov 30, 2015 at 3:25 vote accept Brando
Nov 30, 2015 at 3:24 vote accept Brando
Nov 30, 2015 at 3:25
Nov 30, 2015 at 3:16 history answered Fan Zheng CC BY-SA 3.0