Let & € N. Prove by using the contra-positive that if ³ is odd then is odd. Proof: Choose which of the following statements supports this premise: [Select] [Select] x=2a implies x^3=8a^3=2(4a^3) x=a implies x^3=a^3 x=3a implics x^3-27a^3-3(9a^3)

Q: x - 1 is a factor of x^100 – 1. O False O True O none of the choices

A: x100-1

Q: 6. What should be added from 2x +3x` -- x² -1, so that it becomes exactly divisible by (x-2)?

A:

Q: for x belonging to Z,  prove or disprove 2x^2 +x +1 must have a remainder 1, 4, or 5 when divided by…

A: Given statement is false

Q: 5 ¹ (²³) = O t^(6)/36 O t^(5)/24 O None of them O t^(4)/6

A: The given inverse Laplace transform is .We have to find the inverse Laplace transform.

Q: Evaluate (6 – 5)^2 by working within the parentheses first. Evaluate 6^2 – 5^2. Compare the answer…

A: Evaluate (6 – 5)^2 Evaluate 6^2 – 5^2.

Q: (a) (2x*y')(-x*y) (b) (2х- Зу)(3х - у) 4.(a)_ 4.(b)_ 4.(c)_ 4.(d) (e) (x-y)(x² + xy+ y°) OHER 4.(e)_

A: As we know from the exponent rule; 1). am·an=am+n 2). aman=am-n   (a). Given: 2x4y3-x5y

Q: Determine whether x^5 + 2x^2 + 1 is reducible over Z13

A:

Q: n>=0

A: According to the question,    False. This statement is not true for all integers n >= 0. A…

Q: a. Without tables, show that -(p v (-p ^g)) a nd -p ^-q are logically equivalent.

A:

Q: Answer True or False

A: In the given question we have to check whether the following identity is true or false

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Q: Prove a^2 +4a+3 is odd if and only if a is even.

A:

Q: Prove the claim that there are no integers j and k such that j^2 + 3k^2 = 8

A: Since both j and k are being squared so if we prove the case for positive integers, that will prove…

Q: Suppose that 2^n − 1 is prime. Show that n must also be prime. (Hint: try to find a convenient…

A: Given that 2n-1 is prime. To prove that n must also be prime. On the contrary let us assume that n…

Q: Suppose the following theorem is proven using a direct proof. Theorem: If x is a real number and x…

A:

Q: Express x8 - x as a product of irreducibles over Z2.

A: The given polynomial x8-x. We have to write the polynomial as a product of irreducibles over ℤ2.

Q: A. TRUE OR FALSE. Determine each of the following statements if it is true or false. Support your…

A: Given: 1. P is a prime such that p divides a2 then p divides a 2. If  a3 divides c2, then a divides…

Q: By considering uniqueness of factorization of integers, find all pairs (x, y) ∈ N^2 such that x^2 −…

A:

Q: Prove the following using a direct proof.  If a,b, and c are integers such that b is a multiple of…

A:

Q: Please help quick thanks

A:

Q: When dividing x^3+2x+4 by 3x+2 in Z7[x], the remainder is * O 4 O None of the choices 2.

A:

Q: Prove that m^3 + 2n^2 =36 has no solution in positive integers.

A: Prove that  there is no solution for positive integers.Let if for for

Q: 3. Prove that any Integens . Proof (by contradicton): ,9 t (a?-3)

A:

Q: 28000 +38000 + 48000 + 58000 + 68000 Prove that 1 8000 is a multiple of 13 using Fermat's Little…

A: Given that                                 we have to prove that it is multiple of 13 by using…

Q: Show by induction that 4 divides 2m^2 +6m for an integer m>0

A:

Q: Express (2ry+ 2x- 1)-i (x2 - y-2y) as polynomial in the binomial argument z = x+ iy. O iz? + 2z + 1…

A:

Q: (x3y4z6)7/(x6y4z)6=yrzs/xt Finding the values of r,s,t which are exponents.  I am able to expand…

A:

Q: Let a be an integer such that the remainder of dividing a by 17 is 15. What is the remainder of…

A: We will find out the required value.

Q: Express x8 - x as a product of irreducibles over Z2.

A: Given polynomial is fx=x8-x. To Express: The given polynomial fx=x8-x as a product of irreducible…

Q: Prove by weak induction that (7^n) – 1 is a multiple of 6 fo

A: To prove that by weak induction 7n-1multiple of 6 for alln∈ℕ.