Re: Order modulo p^n (Number Theory)

On Sep 14, 3:56 pm, "dark.sorrow.myst...@xxxxxxxxx"
<dark.sorrow.myst...@xxxxxxxxx> wrote:
Hello need some help with a question in number theory im attempting

Let p be an odd prime and n > 1 an integer. Find the order of (1 + p)
modulo (p^n).

Cheers

***********************************************************

Hints:

1.- Try with p = 3, 1 + p = 4 and n = 1, 2, 3, 4, and then with p = 5
and 1 + p = 6, and then even with p = 7 and 1 + p = 8...

2.- Now prove your guess or huntch: use Newton's binomial with

(1 + p)^(p^(n-1))...you may want to show that the binomial

coefficient [p^r : r] is divisible by p iff r is a multiple of p...

Regards
Tonio
.

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