course Mth 151
Dr. Smith,I wrote you a few times with questions and no reply that is why this is late. Let me know what you think I told you about my problem. Talk to you soon
Exercise 5.1
3. false, 2 can be prime.
5. False
6. False
9. False
10. True
12. True
15. 1,2,4,5,10,20
18.86,43
20.no
21. no
24.no
25. 14X7=98
b. 13
c. Square root, square root, square root
27. 2 and 3, not between 1 and 100
30. 456,882,320 /16=28555145/16=
This problem is not divisible by 16. Because at least one answer is going to have a 5 in it, this number is not divisible by 16 or any of the other numbers mentioned. It will be divisible by 10 or 20 but even 2 eventually get a decimal.
33. 2/240=120/2=60/2=30/2=15/3=5
2 to the 4th . 3.5
35. 360/2=180/2=90/2=45/3=15/3=5/5=1
36.425/5=85/5=17
39. No, it becomes a decimal on the first try
40. 409311, this becomes a decimal after the second division by 7, it is evenly divisible by 9.
42. 287,842, NO, becomes a decimal
45. NO, becomes a decimal.
48. There are infinitely many primes according to Euclid. No matter how large a prime is identified there are always others even larger. This is one of the more elegant proofs in mathematicsIt is called a Proof by contradiction.
50. The unique product of primes is called a prime factorization.
51. 0,2,4,6,8
54. 0,5
55.0,6
57.6
60.144= 9X16, 8X18,12X12,6X24, 3X48,48X3, 4X36
9,16,8,18,12,6,3,48,4,36
63. 1776 is a leap year
65. 2400 leap year
66.1800 leap year divisible by 4
69. This is not always. Numbers like 102,108,114,are all divisible by 6 then however you get 126 but that dioes not happen again until 156.
70. It works ionce for each number, the second time in each case it becomes a decimal. It is because 7,11,and 13 are prime being divisible by themselves and 1.
72. a. Eulers formula does not work for 42. B. Eulers formula works well for 43.
80.30031,This is composite.
81. This concerns Euclids proof by contradiction, it is an elegant mathematical proof and always demonstrates its desired result.
84.
85. 2p-1
87.3,31
Exercise 5.2
3.True
5. True
6. True
9. True
10.True
12. 1+2+4+8+16+32+64+127+254+508+1016+2032+4064=8128
1+2+4+8=15+16=31+32=63+64=127+127=254+254=508+508=1016+1016=2032+2032=4064+4064=8128
15. 1+ ?1/3+1/6=2
18. Abundant
20.Abundant
21.12,18,20, and 24
24.A perfect number is a number equal to its proper divisors.
An abundant number is a number that adds up to less than itself with its proper divisors.
A deficient number is a number is a number that is greater than the sum of its proper divisors.
25. The divisors for 1184 add up to 1210 and the divisors for 1210 add up to 1184. This is why they are friendly!
27. 3+11=14
30. 3+29=32
33. 59,61 and 71,73
35. For 125,111,113 and for 140, 131,133
39. 5 to the 2nd + 2=3 to the 3rd.
42. False
45. one, not happy
48.They did not have the concept of larger numbers in the Billions for example.
50.a. 2X3+1=7 b. 2 and 3 are both prime.
51. B, Sometimes. The text states the primordial formula is a popular place to look for twin primes.
54. 5 2p+1=11 Prime
55. 15, no
57. 27, is not prime
60. n=5 , n-1=4_1=5 n-1 is not prime n+1 is prime
63. B
Exercise 5.3
3. True
5. False
6. True
9.True
10. False
12. 180/2=90/2=45/3=15/3=5
b. 300/2=150/2=75/3=25/5=5
15. 28/2=14/2=7
35/5=7 or 35/7=5
56/2=28/2=14/2=7
18. 130/2=65/5=13
455/5=91/7=13
21. 12/2=6
18/3=6
30/2=15/3=5
24.25/70=2 r20 2/20=10/10=0
25. 84/180=2 r12
27.210/3=70
560/8=70
30. The least common multiple is found by using mXn this only works for two numbers, no more.
33.56/8=7 7X96=672
35. 840
36. can be 288 or 576
39.45/3=15/5=3X75=225
40. 6x60=360
42. 35x2310=80850
45. 84/2=42/2=21/3=7 7x180=1260
48.150/2=75/3=25/5=5 5x480=2400
51. 30
55. 12
57. a. 6 b.36
Exercise 5.4
3.46368
5. 1+ square root of 5 over 2
6. 1.625
9. 1+2+5+13+34+89=144
10. 5 to the 2nd +8 to the second=89
6 to the 2nd +11 to the second=157
12. 11 to the third + 7 to the 3rd ?4 to the third=1610
15. a. 31 +6+1=37 b. 32 +5+3=40 c. 50+2=52
18.
20. This was more of an FYI thing.
21. 176
24.3+7=10, 3+7+18=28 , 3+7+18+29+46=103
25. a. 6x13=78 b. 6x20=120 c. 7+13= 2x10
27. 1x3=3 , 1x2=2x2=4 1 to the 2nd is 1, 2 to the 2nd=4
30.All numbers but 1 and 8 are prime. Primes are divisible by themselves and 1 only. No explanation for 8.
33. .0112359551 and
35. Dr. Smith, I could not find Binet in the index! I was trying to find a reference to i
I can tell you are doing most of these problems correctly, and I believe you'll be OK on the test.
My version of the text differs from yours, so I can't tell what many of these problems are. This is the reason for the Query and q_a_ programs.
I tried to find time to answer the questions you sent me by email, but since they only included chapter and problem number I couldn't answer your questions when I receive them, and when I was near the book I was focused on making timely responses to submitted work.
I won't have the book for the rest of the week. However if you want to send me some information about the questions you had (e.g., descriptions of the problems and what you are thinking about them) I'll be happy to respond.