Let m and n be two relatively prime elements of an Euclidean domain R.
(You may think
R = or
R = [x].)
Let
s, tR be such that
sm + tn = 1.
For every
a, bR there exists cR
such that

(xR) xc mod mn

(1)

where a convenient c is given by

c = a + (b - a) sm = b + (a - b)tn

(2)

Therefore, for every
a, bR the system
of equations