Let a and b be integers. Prove that GCD(a,b) divides GCD(a+b, a−b). Give an example when GCD(a,b) not equals to GCD(a+b, a−b).

Q: him Z Q3. Show that 20Z does not exist.

A: The given problem is to show the given complex limit does not exist.

Q: -7x Sre™-3 + x + x = 1 dx The 3x لوکی

A: Topic:- application of integration

Q: Find the maximum value of a, x, +a,x, + .+ax to the condition that x +x, +. + x =1 for given…

A: We need to find the maximum value of a1x1+a2x2+a3x3+...+anxn to the condition that…

Q: Let a, = 1 and a₁ + a1 = n² + 2n, n ≥2. Evaluate S

A:

Q: 4 (ii) 16 | at + 15.

A: Step-1 1)16|a4+15

Q: Let w be defined as 2 more than the number of digits in the integer w. For example, 15 =4(2 digits…

A:

Q: Show that if ax2 + bx + c = 0 for all x, then a = b = c =0

A: It is given that, ax2+bx+c=0 for all x,  To prove a = b = c = 0

Q: 2. (3x+5)+(2x – 3)

A:

Q: b) Find (3512, 2020) and find integers x and y such that 3512x + 2020y = (3512,2020).

A:

Q: 2 4. Express 989 = 23 43 in the form x² + xy + 5y².

A: The given number is 989. The objective is to express the given number in the form of x2+xy+5y2.

Q: 3. Show that all integers n ≥ 2 can be expressed as 2x + 3y for some nonnegative integers r and y.

A: Mathematical induction is a proof technique used in mathematics to establish the truth of a…

Q: 3. Prove that gcd(a, b) = gcd(3a +56, 11a +186), for any integers a and b. 4. Homework. Suppose…

A:

Q: 1. Show that 2465 is a Carmichael number.

A:

Q: *(2 + 16) (a + 8)(x + 4) 16 where z # a + 8 Submit Question

A:

Q: Show that the operation * on Q – {1}, defined by a * b = a + b – ab for all a, beQ- {1} satisfies…

A:

Q: 1. (a) Prove that if alb and alc. then alb² + 10c + a.

A:

Q: (d) The third quartile for X 提交答案| Tries 0/5 (e) the IQR for X 提交答案| Tries 0/5 (f) P(IX-216|> 41)

A: Given : Let X be a r.v X~N(216 , 18) Here ; μ=216 σ=18

Q: 12 + 22,., +n? =n(n+ 1)(2n + 1), Vn eN

A: We will prove this as following.

Q: 3) Find integers x and y such that 13x + 15y = 1.

A: We see, 15 - 13 = 2              => k(15 - 13) = 2k for any integer k              => 15 k -…

Q: 1. Find two sets of three consecutive odd integers such that the sum of their squares equals 251.…

A: Assume the first odd integer x. Since the integers are consecutive odd integers, then the next two…

Q: Compute the following. 35x4-32x3+15x²–10x+18dx -5

A:

Q: 2. Determine all values of x - y when x and y are integers such that x = 360 + y².

A: The given equation is. x2=360+y2x2-y2=360x+yx-y=360 Since it is given that x and y are integers, so…

Q: 1. Show that 2465 is a Carmichael number.

A: Let n=2465