This question is related to unique factorisation in the Gaussian integers. In the Gaussian integers, find the gcd of 13 and 8 + i. The problem says "the gcd" (which is correct), but what are all the possibilities for the gcd?

Q: Find Im(z) if z(8 + i) = 7+ (384 + 448i)

A:

Q: Suppose that A, B, C, and D are digits from 1 to 9 and that A + B = CD (a) What digit must C be?…

A: Given that  A, B, C and D are digits from 1 to 9 such that  A + B = CD   (a)  If 1 ≤ A, B ≤ 4 then A…

Q: B is not correct

A: We have a condition that n is greater than 1. If we use n=2 as the value we get an equation of u2 +…

Q: Problem 5 Show that am +1 is composite if a and m are integers greater than 1, and m is odd. Hint:…

A: are integers greater than 1.

Q: greatest common divisor(g.c.d)

A:

Q: A number n is divisible by 12 if it satisfies ∃k ∈Z(n = 12k) Give a direct proof that, if n is…

A:

Q: 19 (e) a = 1575, b = -231 (a) 3710

A:

Q: Find a positive integer n such that 2n is a square and 3n is a cube.

A: Sol:- Let 2n be equal to x², where x is a positive integer. Then, n can be written as n = x²/2.…

Q: 3. Let a and b be positive integers. Express the positive greatest common divisor of a and b in…

A: The positive greatest common divisor (gcd) of two positive integers, a and b, can be expressed in…

Q: (7) Recall that vp(n) denotes the highest power of the prime p that divides the nonzero integer n.…

A: Given that denotes the highest power of the prime p that divides the nonzero integer n.First we have…

Q: Factor each of the following a) x-xー4a b)xペー64

A:

Q: 5. For how many different integers bis the polynomial x² + bx + 16 factorable over the integers?

A: From the given data

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: Prove the following: There exist no integers a and b for which 14a + 4b = 1. Please explain the…

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: 1 Use the factorization A = PDP' to compute A^, wherek represents an arbitrary integer. а 11(b - а)…

A:

Q: Use the factorization A = PDP to compute AK, where k represents an arbitrary positive integer. - 7…

A:

Q: Suppose a, b are relatively prime integers. (a) Show that gcd(8a, 8b) = 8. (b) Show that d = gcd(a +…

A: We will use the fact that if a,b are relatively prime integers, then : gcd(a, b) = 1

Q: Show that if a and b are coprime integers, then gcd(a + b, a² – ab + b²) = 1 or 3.

A:

Q: For Theorem 2.8 and it corollary give a simplified and short example in order to explain it very…

A:

Q: For the pair of integers 315 and 825: (a) Find the prime factorization of each number. (b) Find the…

A: As per our company guidelines we are supposed to answer only first three sub-parts. Kindly repost…

Q: prove that the one's digit of any integer,n, is the remainder when one divides n by 10.

A:

Q: How do you prove this?

A: