sum of two elements in a ring Suppose I have a commutative ring $R$ with unity.
And suppose we have three elements $a, b, c \in R$
such that $a+b = c$.
Is it possible that there are two units $\epsilon, \epsilon'$ (not both $1$)
such that $\epsilon a + \epsilon'b = c$?
Thanks!

Take $R=\Bbb {Z/8Z}, a=1, b=2, c=3, \epsilon=1, \epsilon'=5$  
If $b(\epsilon'-1)=0$ (among other ways) you are there.
