# Modular Help

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 :]

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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
break
return zero_divisors


Here is some sample output:

sage: number_of_zero_divisors(2*3*5)
21
sage: number_of_zero_divisors(5*7*11)
144

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