Hey Sonifa.
What is the ordp function for those unfamiliar with it?
Solve the following :
a) Show that
ordp((p^n)!)=1+p+p^2+p^3+....+p^(n-1)
b)For which values of p does the
following series converge in
Qp?
1)1+(15/7)+(15/7)^2+(15/7)^3+......
2)1!+2!+3!+4!+....
For
a) I wanna to count how many terms of (p^n)! containing the factor p but I
failed using my way.
For b) 1) I tried to use the definition of
convergent in Qp but when i got the geometric series then it is complicated to
analyse p and 2) I have no idea
Can someone help me ?? many
thanks
Consider the set . Every p integers is divisible by p. There are such numbers. Every integer divisible by is also divisible by , so you need to cound those numbers an additional time (since the factorial takes a product of all of those numbers). There are integers with as a factor. And in general, there are integers with as a factor. So, add that all up:
For b) hint: (1) the answers should be 3 and 5. (2) all p
Edit: for b) (1), I think works, too