and

and | ||

and and |

defined by

mod mod

**The map is injective:** If
, then
and
, so, since
,
, so .

**The map is surjective:** Given with
,
, the Chinese Remainder Theorem implies that there
exists with
and
. We
may assume that
, ans since
and
, we must have
. Thus
.

Because is a bijection, the set on the left has the same size as the product set on the right. Thus

? eulerphi(389*11^2) %15 = 42680