Thm 22 :
a = bmodm
Let a bicid
,
myO be integers
,
and
C = d mode
,
Show
b +d
a +c =
Py
:
a =
By the division theorem
gam
+
C
r,
qcrr2
=
d
b = abm + r
,
qdM + 12
=
(aa qc)m (r, rz)
b d (ab qd)m (v +2)
a+c
+
=
+
+
=
+
S
m((a c)
-
+
By thm 21
(b +d)
a + c = b +d
1 + 5
11 + 17
11-3
+
+
.
S
(modm)
mod 12
z
=
4
mod 12 = 4
mod
12 =
9