Ask Your Question

Modular Help

asked 2010-12-10 02:31:05 +0100

valgal210 gravatar image

Quick question. I know that the number of units + number of zero divisors + 1 = n for Z mod n. When n is the product of three distinct primes, how can I make the coding so Sage will return the number of zero divisors. I'm at a standstill and would appreciate any help. Thanks :]

edit retag flag offensive close merge delete

1 Answer

Sort by ยป oldest newest most voted

answered 2010-12-10 02:59:08 +0100

Mike Hansen gravatar image

This seems more like a homework question than something about Sage. Sage won't be able to give you a formula for the number of zero divisors of Z mod (pqr) (although one exists); you need some more theoretical knowledge for that. However, here is a naive function which counts the number of zero divisors of Z mod n:

def number_of_zero_divisors(n):
    zero_divisors = 0
    for i in range(1, n):
        for j in range(1, n):
            if (i*j) % n == 0:
                zero_divisors += 1
    return zero_divisors

Here is some sample output:

sage: number_of_zero_divisors(2*3*5)
sage: number_of_zero_divisors(5*7*11)
edit flag offensive delete link more

Your Answer

Please start posting anonymously - your entry will be published after you log in or create a new account.

Add Answer

Question Tools


Asked: 2010-12-10 02:31:05 +0100

Seen: 287 times

Last updated: Dec 10 '10