In this paper the following result is proved. Let r, s and n be integers satisfying
0
⩽
r
>
s
>
n
0 \leqslant r > s > n
,
s
>
n
1
/
3
s > {n^{1/3}}
,
gcd
(
r
,
s
)
=
1
\gcd (r,s) = 1
. Then there exist at most 11 positive divisors of n that are congruent to r modulo s. Moreover, there exists an efficient algorithm for determining all these divisors. The bound 11 is obtained by means of a combinatorial model related to coding theory. It is not known whether 11 is best possible; in any case it cannot be replaced by 5. Nor is it known whether similar results are true for significantly smaller values of
log
s
/
log
n
\log s/\log n
. The algorithm treated in the paper has applications in computational number theory.