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Задание
64.
Найти
действительное
число
,
которое
имеет
данное
представление
в
виде
периодической
цепной
дроби
.
1.
[3; 3, 1, (2)].
2.
[2; 1, 5, 2, 1,(2, 1)].
3.
[4; (1, 3, 1, 8)].
4.
[2; (1, 1, 1, 4)].
5.
[2; (1, 4)].
6.
[3; (3, 6)].
7.
[3; (1, 2, 1, 6)].
8.
[–1; 3, (1, 2)].
9.
[4; (4, 8)].
10.
[–1; 5, (1, 4)].
11.
[3; (2, 6)].
12.
[3; (1, 1, 1, 1, 6)].
13.
[3; (1, 6)].
14.
[4; 3, (2, 4)].
15.
[5; (2, 1, 1, 2, 10)].
16.
[1; 2, (3, 4)].
17.
[4; (3, 2)].
18.
[(5; 4, 3)].
19.
[(2; 6, 1)].
20.
[3; 1, (2, 3)].
21.
[3; (2, 5)].
22.
[(3; 2, 5)].
23.
[(3; 2, 1, 4)].
24.
[(3; 1, 4)].
25.
[(1; 6, 5, 6)].
26.
[4; (1, 3, 1, 8)].
27.
[2; (3, 1)].
28.
[4; (2, 8)].
29.
[4; (1, 1, 2, 1, 1, 8)].
30.
[2; (1, 7)].
Задание
65.
Решить
сравнение
первой
степени
с
помощью
цепных
дробей
.
1.
32
x
≡
63(mod 119).
2.
69
x
≡
192(mod 201).
3.
37
x
≡
5(mod 217).
4.
271
x
≡
25(mod 119).
5.
91
x
≡
143(mod 222).
6.
143
x
≡
41(mod 221).
7.
82
x
≡
14(mod 202).
8.
354
x
≡
567(mod 639).
9.
67
x
≡
64(mod 183).
10.
89
x
≡
86(mod 241).
11.
213
x
≡
137(mod 516).
12.
111
x
≡
81(mod 447).
13.
186
x
≡
374(mod 422).
14.
129
x
≡
321(mod 471).
15.
–50
x
≡
67(mod 177).
16.
–73
x
≡
60(mod 311).
17.
–53
x
≡
84(mod 219).
18.
143
x
≡
75(mod 119).
19.
13
x
≡
178(mod 153).
20.
243
x
≡
271(mod 317).
21.
221
x
≡
111(mod 360).
22.
141
x
≡
73(mod 320).
23.
139
x
≡
118(mod 239).
24.
327
x
≡
78(mod 379).
25.
239
x
≡
302(mod 471).
26.
23
x
≡
667(mod 693).
27.
57
x
≡
15(mod 482).
28.
21
x
≡
15(mod 111).
29.
15
x
≡
120(mod 851).
30.
2560
x
≡
45(mod 3605).

66
Задание
66.
Решить
сравнение
.
1.
6
x
10
–12
x
+1
≡
0(mod

5).
2.
x
5
–2
x
3
+
x
2
–2
≡
0(mod

3).
3.
x
5
–7
x
4
+9
x
2
–
x
+13
≡
0(mod

3).
4.
x
7
–
x
6
+5
x
2
–3
≡
0(mod

5).
5.
x
5
+
x
4
+
x
3
–
x
2
–2
≡
0(mod

5).
6.
x
7
–6
≡
0(mod

5).
7.
x
8
+2
x
7
+
x
5
–
x
4
–
x
+3
≡
0(mod

5).
8.
6
x
4
+17
x
2
–16
≡
0(mod

3).
9.
4
x
7
–2
x
3
+8
≡
0(mod

5).
10.
x
7
–2
x
6
+2
x
2
+13
≡
0(mod

5).
11.
x
12
+2
x
11
–2
x
–1
≡
0(mod

11).
12.
x
10
+
x
8
+
x
7
–
x
4
–
x
2
+4
x
–3
≡
0(mod

7).
13.
x
29
+3
x
15
+
x
11
–3
x
5
+9
x
2
+10
x–
5
≡
0(mod11).
14.
x
12
–2
x
7
+
x
3
+1
≡
0(mod

5).
15.
x
14
–4
x
13
–
x
+6
≡
0(mod

13).
16.
x
12
–2
x
7
+
x
3
+1
≡
0(mod

5).
17.
13
x
23
–8
x
22
–2
x
13
+1
≡
0(mod

11).
18.
10
x
91
+
x
11
+9
x
2
–
x
+6
≡
0(mod

11).
19.
10
x
42
–5
x
30
+2
x
2
+4
≡
0(mod

17).
20.
28
x
9
+
x
8
–28
x
7
+
x
4
+23
≡
0(mod

3).
21.
34
x
10
+
x
7
+3
x
4
+
x
+37
≡
0(mod

5).
22.
x
12
–53
x
11
–24
x
6
–
x
+1
≡
0(mod

7).
23.
x
10
–2
x
+1
≡
0(mod

5).
24.
x
8
+2
x
7
–
x
4
+3
≡
0(mod

5).
25.
x
16
+3
x
8
–
x
4
+
x
–2
≡
0(mod

7).
26.
x
10
+
x
8
–
x
4
–
x
2
+5
x
–3
≡
0(mod

7).
27.
x
101
+6
x
5
+9
x
2
–5
≡
0(mod

11).
28.
x
14
–
x
13
–
x
2
+2
x
+1
≡
0(mod

13).
29.
323
x
90
+164
x
67
–1
≡
0(mod

23).
30.
2
x
35
–9
x
15
+13
x
8
+
x
+5
≡
0(mod11).
Задание__67.'>Задание
67.
Найти
порядок
элемента
а
по
модулю
m.

1.
a
=
6,
m
=
23.
2.
a
=
3,
m
=
25.
3.
a
=
7,
m
=
29.
4.
a
=
27,
m
=
47.
5.
a
=
2,
m
=
17.
6.
a
=
5,
m
=
17.
7.
a
=
10,
m
=
13.
8.
a
=
10,
m
=
31.
9.
a
=
13,
m
=
53.
10.
a
=
18,
m
=
29.
11.
a
=
5,
m
=
61.
12.
a
=
10,
m
=
47.
13.
a
=
32,
m
=
61.
14.
a
=
32,
m
=
71.
15.
a
=
2,
m
=
35.
16.
a
=
3,
m
=
55.
17.
a
=
10,
m
=
17.
18.
a
=
97,
m
=
17.
19.
a
=
18,
m
=
11.
20.
a
=
23,
m
=
41.
21.
a
=
6,
m
=
59.
22.
a
=
14,
m
=
59.
23.
a
=
3,
m
=
17.
24.
a
=
3,
m
=
19.
25.
a
=
5,
m
=
18.
26.
a
=
5,
m
=
23.
27.
a
=
18,
m
=
41.
28.
a
=
8,
m
=
19.
29.
a
=
15,
m
=
23.
30.
a
=
18,
m
=
23.

Задание
68.
Решить
сравнение
с
помощью
индексов
.
1.
2
x
≡
7(mod 67).
2.
13
x
≡
12(mod 47).
3.
x
27
≡
39(mod 43).
4.
8
x
26
≡
37(mod 41).
5.
25
x
7
≡
–7(mod 31).
6.
20
x
≡
21(mod 41).
7.
37
x
15
≡
62(mod 73).
8.
5
x
4
≡
3(mod 11).
9.
2
x
8
≡
5(mod 13).
10.
2
x
3
≡
17(mod 41).

67
11.
27
x
5
≡
25(mod 31).
12.
11
x
3
≡
6(mod 79).
13.
23
x
3
≡
15(mod 73).
14.
52
x
≡
38(mod 61).
15.
37
x
8
≡
59(mod 61).
16.
18
x
8
≡
6(mod 13).
17.
x
12
≡
37(mod 41).
18.
x
55
≡
17(mod 97).
19.
x
35
≡
17(mod 67).
20.
x
30
≡
46(mod 73).
21.
x
8
≡
23(mod 41).
22.
x
5
≡
74(mod 71).
23.
16
x
≡
11(mod 53).
24.
x
8
≡
29(mod 13).
25.
12
x
≡
17(mod 31).
26.
13
x
8
≡
–36(mod 61).
27.
7
x
13
≡
–23(mod 47).
28.
19
x
5
≡
–13(mod 53).
29.
23
x
≡
37(mod 41).
30.
5
x
11
≡
–19(mod 29).
Задание
69.
Представить
многочлен
f
(
х
)
по
степени
двучлена
х
–
α
.

1.
f
(
x
) =
x
3
–8
x
2
+23
x
–24,
α
= 2.
2.
f
(
x
) =
x
4
–7
x
3
+3
x
2
+63
x
–108,
α
= 2.
3.
f
(
x
) =
x
5
–4
x
3
+6
x
2
–8
x
+10,
α
= 2.
4.
f
(
x
) =
x
4
–2
x
2
+3,
α
= –1.
5.
f
(
x
) = 2
x
3
+13
x
2
+25
x
+14,
α
= –2.
6.
f
(
x
)=3
x
4
+24
x
3
+70
x
2
+87
x
+38,
α
=–2.
7.
f
(
x
) =
x
4
–8
x
3
+24
x
2
–50
x
+90,
α
= 2.
8.
f
(
x
) =
x
5
,
α
= 1.
9.
f
(
x
) =
x
3
–9
x
2
+27
x
–27,
α
= 3.
10.
f
(
x
) =
x
3
–5
x
2
+3
x
+9,
α
= 3.
11.
f
(
x
) = 2
x
3
–18
x
2
+108,
α
= 3.
12.
f
(
x
) = 3
x
3
–81
x
+162,
α
= 3.
13.
f
(
x
) =
x
4
–12
x
3
+54
x
2
–108
x
+81,
α
= 3.
14.
f
(
x
) =
x
4
–6
x
3
+18
x
2
–54
x
+81,
α
= 3.
15.
f
(
x
) =
x
4
+3
x
2
+1,
α
= –1.
16.
f
(
x
) = 2
x
5
–
x
3
–2
x
2
–6
x
+10,
α
= 2.
17.
f
(
x
) = 4
x
3
–2
x
2
+5
x
–1,
α
= 2.
18.
f
(
x
) =
x
4
–4
x
3
+5
x
–2,
α
= 3.
19.
f
(
x
) =
x
4
+7
x
3
+4
x
2
–25
x
+1,
α
= –5.
20.
f
(
x
) =
x
4
–8
x
3
+24
x
2
–50
x
+22,
α
= 2.
21.
f
(
x
) =
x
4
+3
x
3
–4
x
2
+6
x
–5,
α
= –2.
22.
f
(
x
) = 2
x
5
–3
x
3
+6
x
2
–8
x
–4,
α
= 3.
23.
f
(
x
) = 4
x
3
–2
x
2
+5
x
+11,
α
= 2.
24.
f
(
x
) = 3
x
4
+8
x
3
–2
x
2
+6
x
–5,
α
= –3.
25.
f
(
x
) =
x
4
+2
x
3
–3
x
2
–4
x
+1,
α
= –1.
26.
f
(
x
) =
x
5
–5
x
4
+7
x
3
–2
x
2
+4
x
–8,
α
= 2.
27.
f
(
x
) =
x
5
+9
x
4
+32
x
3
+57
x
2
+51
x
+18,
α
= –2.
28.
f
(
x
) =
x
6
–12
x
5
+60
x
4
–161
x
3
+246
x
2
–204
x
+72,
α
= 2.

68
29.
f
(
x
) =
x
5
–11
x
4
+49
x
3
–111
x
2
+129
x
–63,
α
= 2.
30.
f
(
x
) =
x
6
+12
x
5
+59
x
4
+152
x
3
+215
x
2
+156
x
+45,
α
= –2.

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