Question

Arithmetic Derivative playing around @Marki

Answer 1

lol wanna prove it here ?

Answer 2

It's pretty fun to notice that: \[\LARGE (p^p)'=p^p\]

Answer 3

I don't know if it's worth proving if we believe it. Tell me your doubts if you have them.

Answer 4

i dont simply believe i only thought its interesting to show

Answer 5

Look back on the example I gave in the last one for(2^4)'=4*2^3 since it makes it pretty clear that it will be true if you walk through this calculation on your own.

Answer 6

i just proved it on my note xD

Answer 7

But I can give you a proof. It's just I generally find proofs to not be very good at explaining things.

Answer 8

lol

Answer 9

Oh ok, good. So now let's talk about finding \[\LARGE \gcd ( n,n')\] and adding them all up from 1 to 5*10^15 haha

Answer 10

i used this fact