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The equation
can have no solutions if
since then
for any
. So assume
that
.
We first consider the case
. Then we can find and
such that
(use the Euclidean
algorithm to get and
such that
).
Then put
so
. Any other
solution is congruent to
, as
and
.
So if then a solution exists and is unique modulo .

root
2002-06-10