# Im soooooo close to solving this problem (Rings)

1. Apr 27, 2007

### nick727kcin

Let R be a ring of characteristic m > 0, and let n be any
integer. Show that:

if 1 < gcd(n,m) < m, then n · 1R is a zero divisor

heres what i got out of this:

Let gcd(n,m) = b

1< d < m so m/d = b < m
and d | n

Also, m * 1_R = 0

can someone please offer some insight?
thanks,
nick

2. Apr 27, 2007

### Data

You know $m 1_R=0_R$. You need to show that there are some x, y in R with $x\cdot (n 1_R) = 0_R$ and $(n 1_R) \cdot y = 0_R$.

I suggest trying $y=x = \frac{m}{(n,m)}1_R$.