Our migration from 5.3sp1 to 2011sp1 will happen for period of 2-3 months, but content will be added on production during that time in tridion 5.3sp1. 
After the migration activities we will have migrated system on 2011sp1,  

But now i want to migrate new content from production(which is still in 5.3) to upgraded DB.

Content porter version 2.3(currently being used in 5.3sp1 ) is not supported in 2011.

What would be the best approach for this?


Question: Prove that a primitive root of $p^2$ is also a primitive root of $p^n$ for $n>1$.
Answer: We know from here, if $ord_pa=d, ord_{(p^2)}a= d$ or $pd$

If $a$ is a primitive root $\pmod {p^2}, ord_{(p^2)}a=\phi(p^2)=p(p-1)$ 

Then $ord_pa$ can be $p-1$ or $p(p-1)$

But as $ord_pa&lt;p, ord_pa$ must be $p-1=\phi(p)\implies a$ is a primitive root $\pmod p$

Again from here, $$ord_{(p^s)}(a)=d, ord_{p^{(s+1)}}(a)=pd,\text{ then } ord_{p^{(s+2)}}(a)=p^2d$$

So, as $ord_pa=p-1,ord_{(p^2)}a=p(p-1); ord_{(p^3)}a$ will be $p\cdot p(p-1)=\phi(p^3)$

Again as,  $ord_{(p^2)}a=p(p-1) ord_{(p^3)}a=p\cdot p(p-1);ord_{(p^4)}a$ will be $p\cdot p^2(p-1)=\phi(p^4)$