State the Division Algorithm and use it to find q and r for each of the followin

Question

State the Division Algorithm and use it to find q and r for each of the following pairs of a and b a = 200, b = 7 a = -5,6 = 12 a = 0,b = 13 a = 13, b = 0 Extending the Division Algorithm to polynomials find the quotient and remainder when x3 - 4x2 + 7x - 1 is divided by 2x2 - 3x + 4 Using the fact, from Euclid's Algorithm, that there are integers x and y so that the greatest common divisor of a and b equals ax + by, prove that if n is any common divisor of a and b, then n divides gcd (a, b). Showing your work by hand use Euclid's algorithm to find gcd(2235,495) Show your work by hand use Euclid's algorithm to show that 751 and 215 are coprime, and to find x and y such that 751x+215y=l. Using a spreadsheet (or by hand if you really want to) use the extended Euclid's Algorithm, aka the Pulverizer, for a = 24657 and b = 376, copy the whole worksheet onto the test. The following problem is to be worked in Z7 List the elements of Z8 3 4 4 4 1 3 4 divided by 3. (I don't know the command for the division circle sign) List all the elements that have a multiplicative inverse. Solve, showing your work, Ax - 5 = 2 mod(13)

Explanation / Answer

1. c 2. Q = 5; R = 8.5 3. Suppose it is desired to find gcd(1989, 867), i.e. the greatest common divisor of 1989 and 867. If we reduce the larger number by subtracting the smaller one from it, the gcd does not change: So subtract again: Now 867 is no longer the smaller number. Continuing in the same way, we reduce the larger number, now 867, by subtracting the smaller one from it, leaving the gcd unchanged: The first number, 255, is still the smaller one, so again we use it to reduce the larger one: Now 255 is the larger number and we reduce it by subtracting 102 from it: Now 102 is the larger one and we reduce it by subtracting 51 from it: Now we are done: we conclude that gcd(1989,867) = 51. Thus we must have By division, we get 7. b

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.