Section
4.4
91
Exercises 4.4
1. (a) [BB] 5,12,19,
2,
9, 16 are in 5. 4,11,18, 3, 10,
17 are in
3.
(b) [BB] The general element of
5
is an integer of the form
7k
+
5 for some integer
k.
The general
form of an element in
3 is an integer of the form
 3 for some integer
k.
2. (a) 3,16,29,42, 10, 23, 36, 49, 62 are elements of 3.
11,24,37,50,
2, 15, 28, 41, 54 are elements of
2.
(b) The general integer in
3
is of the form
13k
+
3 for some integer
k.
The general integer in
2 is of
the form
13k
 2 for some integer
k.
3. (a) [BB] 1286 = 32(39)
+
38, so 1286 (mod 39) = 38.
(b) 43,197 = 129(333)
+
240, so 43,197 (mod 333) = 240.
(c) [BB] 545,608 = 10,699(51)
+ 41,
so 545,608 (mod 51) = 41.
(d) 125,617 = 399(315)
+
68, so 125,617 (mod 315) = 68.
(e) 11,111,111,111 = 10,001,000(1111)
+
111, so 11,111,111,111 (mod 1111) = 111.
4. (a) [BB] False: 18  2 = 16 is not divisible by 10.
(c) [BB] True: 44  (8)
=
52 is divisible by 13.
(b) True: 13 
7
=
20 is divisible by 5.
(d) False: 423 
17 = 406 is divisible by 29, so 17 = 423.
(e) False: 400  (18) = 418 is divisible by 19.
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This note was uploaded on 11/08/2010 for the course MATH discrete m taught by Professor Any during the Summer '10 term at FSU.
 Summer '10
 any
 Graph Theory

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