eminent 19thCian Sophie Germain (see the HighlightGermain primes?History in this section). Which of 11, 13, 97, 241, and 35is a natural number. Argue briefly that if p divides n and q31. Assume that p and q are different prime numbers and that n32. Draw a square measuring 10 centimeters on a side. Drawvertical and horizontal line segments dividing the squareinto rectangles of areas 12, 18, 28, and 42 square cen-timeters, respectively. Where should A, B, C, and D bedivides n, then pq divides n.located?21C0911 701Bsmind einiA2 401 091T 101581 omistDivistD16

Answered: 31. Assume that p and q are different…

31. Assume that p and q are different prime numbers and that n divides n and q is a natural number. Argue briefly that if p divides n, then pq divides n. 32. Draw a sou Draw

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

See similar textbooks

Similar questions

1. find the convolution of П 2 2) *П
9. Classify each of the following statements as true or false where a and b are distinct natural numbers. a. LCM(a, b) |GCD(a,b) b. LCM (a, b) ab c. GCD(a, b) ≤ a d. LCM(a, b) a in and then find GCD(4, 12), which is 4.
8. Use divisibility tests to decide whether the given number is divisible by 2, 3, 4, 5, 6, 8, 9, 10, 11 and/or 12. YOU MUST SHOW ALL WORK TO RECEIVE CREDIT. Please put a O if the factor divides the given number and an X if it does not. 2 3 4 5 6 8 9 10 11 12 555,555,550 50,076 Show ALL work here:
12. The early Egyptian Ahmes Papyrus (1650 B.C.E.) shows how to use a doubling method to divide 696 by 29. (George Joseph, The Crest of the Peacock, 2000, pp. 61-66) Doubles of 29 58 116 232 464 928 Doubles of 1 2 4 8 16 32 Double the divisor (29) until you go past the dividend (696). Find doubles of 29 that sum to 696: 232 + 464 = 696. Then sum the corresponding doubles of 1: 8 + 16 = 24. So 696 divided by 29 is 24. a. Divide 4050 by 225 with this method. @ b. Divide 57 by 6 with this method. (Hint: Use doubles and halves.)
A palindrome is a number that reads the same forward and backward, such as 2,743,472. (a) Give a clear but brief argument showing that every palindrome with an even number of digits is divisible by 11. (b) Is it possible for a palindrome with an odd number of digits to be divisible by 11? Explain. (a) Choose the correct answer below. O A. The sum of the digits will always be a non-zero multiple of 11 and therefore a palindrome with an even number of digits will always be divisible by 11. O B. The sum of the digits will always be 0 and therefore a palindrome with an even number of digits will always be divisible by 11.
5. The GCF of any even number and any number divisible by 3 number is always 6.
58. The integer k is the product of four different prime numbers. If k divided by 22 is a multiple of 13, which of the following could be equal to k divided by 11?
21 pare. 1 5 down the ones. Subtract. 12-10 2 Compare. 2 5 There are no more digits to bring down, so 2 is the remainder. ng. 2. 7)249 3. 5)365 5. 2)499 6. 6)396 you divide 425 by 9 that the first digit
3. Kate was given the following number pattern by her teacher. 22+1=5 42+1=17 62+1=37 102+1=101 14²+1=197 Kate made the following conjecture based solely on the number patterns shown. "When an even number is squared and one is added to it, the resulting number is a prime number". In the examples above 5, 17, 37, 101, and 197 are prime numbers because the only factors of these numbers are 1 and the number itself. a) Is Kate's conjecture True or False, based solely on the numbers shown? Use your understanding of even numbers and prime numbers to explain your answer. b) Determine a counterexample to the pattern above to show that Kate's conjecture is false.
14. How many 4-digit numbers can be formed using digits from {1,2,3,4.5) if repeated digits are allowed? O 525 O none of these O 400 O 210
12 If the largest of 111 consecutive integers is 263, what is the smallest? 153 O 373 152 O 154
How many strings of letters from the set (A, B, C, D, E} are there which have length six, have no repeated letters, and start with the letter 'E' and end with the letter 'A'? O O O 4 × 3 × 2 6x5x4x3 5×4×3×2 None of the other answers listed here is correct. 46 64