given three numbers p , q, r calculate the pow( p , q!) % r
It would also be helpful if you could mention the important concepts needed in solving this problem ,
given three numbers p , q, r calculate the pow( p , q!) % r
It would also be helpful if you could mention the important concepts needed in solving this problem ,
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If $$$p$$$ and $$$r$$$ are relatively prime you use Euler's theorem $$$p^{\phi(r)} = 1$$$ mod $$$r$$$. So you need to calculate $$$q!$$$ mod $$$\phi(r)$$$. $$$\phi$$$ is the Euler totient function, for a prime $$$r$$$ it is just $$$r-1$$$. You can find the answer even if $$$(p, r) \gt 1$$$, but it involves additional steps.
Thanks a lot, could you also mention what else do I have to learn if (p,r)>1 or will Euler totient function suffice?
In that case you could perform prime decomposition of $$$r$$$. Find the remainder for each prime power and then use the Chinese remainder theorem.
Cant' we directly use the generalization??
from this link