Solutions manual for NTB - 2.2 Definitions and basic properties of congruences
Exercise 2.3. Let
with
. Show that
iff
.
Proof
(q.e.d)
Exercise 2.4. Let
with
and
. Also, let
. Show that:
.
Proof
(q.e.d)
Exercise 2.5. Let
with
,
, and
. Show that if
, then
.
Proof
(q.e.d)
Exercise 2.6. Let
with
,
, and
. Show that if
and
, then
.
Proof
(q.e.d)
Exercise 2.7. Let
with
and
. Show that
.
Proof
(q.e.d)
Exercise 2.10. Show that the equation
has no solutions
.
Proof
(q.e.d)