2. Compute the ged of the number below using 1) factorization, 2) using Euclid's division algo- rithm: (a) gcd(24, 15) (b) gcd(172, 20) (c) gcd(54, 21) 3. Using the reverse of Euclid's division algorithm compute: (a) Find integers x, y such that 24r + 15y = 3 (b) Find integers x, y such that 172x + 20y = 1000 (c) Find integers x, y such that 23x + 17y = 1 4. Using your work from the earlier parts or independently find: (a) mod 8 (b) + mod 23 (c) mod 7

Q: 3. Use the Division Algorithm to establish the following: (c) The fourth power of any integer is…

A: See the attachment

Q: If a = 282 and b = 34 then find the followving: 1) Find gcd(a, b) "use Euclidean algorithm" 2) Write…

A: Euclidean algorithm is one of the easiest way of finding gcd of two numbers. According to Euclidean…

Q: (2) (b) (c) Use the Euclidean algorithm to determine the gcd of 85 Write down all the divisors of 85…

A: Let the given numbers are a = 85 and b = 135 (a)    From Euclidean algorithm.…

Q: Use Euclid's algorithm to calculate acd(33 + 35. 332 + 352).

A: I have used Euclid algorithm

Q: A positive integer is divisible by 5, but it leaves remainders of 1 and 7 (resp.) when divided by 3…

A: Here we will use Chinese Remainder Theorem to find solution.

Q: Determine the greatest common divisor GCD (xn-1,Xm-1) where m, n are nonzero natural numbers.…

A: We have to determine the greatest common divisor of xn-1, xm-1, where m, n are nonzero natural…

Q: 1.) Create and solve one equal group problem.

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: (a) Use the division algorithm to show that any number N can be written as either N = 3k, N = 3k +…

A: (a) Use the division algorithm to show that any number N can be written as either N = 3k, N = 3k +…

Q: Given f(x)= -x +2x* -3x + x? -4x + 5. Use Horner's algorithm to compute a. f(-2) b. f(x)/(x+2) C.…

A: (a) We have f(x) = -x6+2x5-3x3+x2-4x+5, and we can rearrange this as f(x) = 5-4x+x2-3x3+2x5-x6

Q: This question is about the division algorithm in Z[√2]. Let w = (-3+8√2) and 2 = (6-7√2). (0) Find…

A: there are some problems in question. Please find the details in next steps

Q: • Applying the division algorithm on a = -20,b = 7 we have A) -20 = (7)(-2) + (-6) B) -20 = (7)(-4)…

A:

Q: 14) Find a remainder after dividing 2300 on 3.

A: We have, 22≡1 (mod 3) ⇒22150=1150( mod 3) ⇒2300=1(mod 3)

Q: For a = 2695, b = 1820, use the prime factorizations to find lcm(a, b) and gcd(a, b). Verify that ab…

A: Given thata = 2695  and   b = 1820We have to find lcm(a, b) and gcd(a, b) by using prime…

Q: Use synthetic division to divide 4x4 – x2 – 19x +7 by x – 2. - Write just the numbers of the 3rd row…

A:

Q: Use the Euclidean algorithm to find the greatest common divisor of 3408 and 2903. Then find…

A: I'm providing hand written solution for better understanding.

Q: 5 find the quotient i15-as a" by long division meth od 1-a

A:

Q: 4) Determine whether each polynomial P is a factor of the polynomial Q. If it is, state the other…

A: To find that P is a factor of Q or not.

Q: 3. Find integers s and t so that 1 7s + 11t. Show that they are not unique.

A: The division algorithm states that for any integer, a, and any positive integer, b, there exists…

Q: Using the Division algorithm determine gcd (82,47), and further, determine integers x and y such…

A: See the attachment

Q: Using the Euclidean Algorithm the number of steps needed to find the greatest common divisor of two…

A: How to Find the GCF Using Euclid's Algorithm Given two whole numbers where a is greater than b, do…

Q: plz help out with these math questions. ANSWER IT WITH 7-8 PARAGRAPHS a) Describe the history of…

A:

Q: Divide using long division. 9x2 - 64 Зх- 8

A:

Q: 1. [K5] Use long division to divide 4x* – 2x² - 1 by x – 1. Then write the associated division…

A:

Q: - Use the division algorithm to find the quotient q and the remainder r when dividing f(x)=x³+x² + 4…

A:

Q: 3. For the numbers 360 and 70, use the Euclidean Algorithm (augmented or otherwise) to find the…

A:

Q: If 4x³ + 9x² - 1 is divided by 2x+1, then the restriction on x is OA) x = 1/2 Q¹ B) x1 O c) * = -…

A: Given: Multiple choice questions. Question 1) If 4x3+9x2-1 is divided by 2x+1, then restriction of x…

Q: Find the smallest positive integer N≥ 2 that gives remainder 1 upon division by each of the integers…

A:

Q: The remainder upon the division of x98 +4 by x - 2 in z, is:

A: We have to use remainder theorem.

Q: The remainder upon the division of x98 +4 by x - 2 in z, is: 6. None

A: