mod unknown in a list of equations with all knowns If I have these equations
$a = b \bmod c$ and 
$d = e \bmod c$ and
$f = g \bmod c$
all are known except $c$
can I solve for $c$?
ie: is there a unique solution assuming all $a,b,d,e,f$ are not equal

In general, the solutions for $c$ are all those $c$ such that
$$
\newcommand{\div}{\; \mid \;}
c \div b - a, e - d, g - f
$$
i.e.
$$
c \div \gcd(b-a, e-d, g-f)
$$
Thus there is a unique solution if and only if
$$
\gcd(b-a, e-d, g-f) = 1.
$$
