Let p be a prime, a ∈ Z. Prove that ap − a is divisible by p.

Q: Find T(v) by using the standard matrix and the matrix relative to B and B'. T: R² R², T(x, y) = (2y,…

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Q: The answer is incorrect because the question requires to prove it without fully expand the terms.…

A: This question can be solved using the concept of general term of binomial expansion.

Q: Q3 Prove that In Coth x 1

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Q: Required information NOTE: This is a multi-part question. Once an answer is submitted, you will be…

A: Proof that (iii) implies (i)Step 1: Suppose 3x - 1 is rational.Step 2: So, 3x−1=pq where p and q are…

Q: 6. Find all the roots of the following polynomials: a) p(r) = * - 3.r" +?+ 7x – 30 and b) p (r) = r*…

A: Note: Since we are allowed to solve one question at a time, we have solved the first one. Kindly…

Q: 6 (iv) (v) (8) 5

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Q: If A = {r|- 23 < x < 3how many negative integers does Acontain? Note that: 'I' means 'Such that'

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Q: Example Solve z"+ 512U3+ j512=0 or Find all the roots of fl3)=2"+572V3+j5]2. 10 on What ure the ten…

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Q: 3. Invent two interesting and original positive integers a and b. Let f(x) = ax +3. (a) (b) What is…

A: Given function is fx=ax+3. To find:  a  f10   (b). A number x such that fx=b Solution: Given…

Q: e O Di) what's A B c) A) B) another (-1+73)/10 (1 - 1) /2 (1-7) / 8 (-1 +7i)/4 f(x) has a f(x) f(x)…

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Q: \2 ) **-8 =O x38

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Q: Which of the following is a 4th root of -1.25-12.3? 0.9931 +j 0.8113 O 1.4454-j 0.4312 -0.5569-j…

A: The given problem is to find the fourth root of the given complex expression. Given complex…

Q: Use Fermat's Theorem in your proof that Vn E Z>², 2 is irrational. I

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Q: ply DeMorgan's Laws un - && (Ir || a))

A: Introduction: The formula for de morgan's law is given by, ~(a∧b)=~a∨~b~(a∨b)=~a∧~b

Q: Find a real root of x³2x-1=0 which lies between 1 and 2 by using Bisection method correct to 2…

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Q: Can someone please help me understand the following problem. I need to know how to start the…

A: Zero divisors in a ring Z is an element a (non zero element), such that ab=0 where b is a non zero…

Q: QUESTION 3 Let P(x) is cold Q(x,y)=xisy. The universe of x is seasons, and the universe of y is…

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Q: 1. You want to prove the following formula by induction. n Σ(2i + 2) = n(n+3) i=1 (a) Complete the…

A: Given  ∑i=1n2i+2=nn+3 Basis step: Prove the result for n=1. Inductive Step: Assume the result is…

Q: 3 4 gla) - 4 17 3 A) s '(x) 3 A) Yes B) No -2.x + 8 B) f (x) – 3 C) s '(x) – x – 1 2 3) Sl:) – VI+2…

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Q: 2 Express ( √5 - √5₂) in 2 simplest a + bi form.

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Q: MPLETION. Fill-out the missing information on the table, perform the necessary operations. Show your…

A: Note- Since you have posted a question with multiple sub-parts, we will solve first three sub-parts…

Q: By using Caushy Rieman prove that (2) and (3) (2) 4c2) = (3) prove That (3)- 3.

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Q: (a) Convert the number 1217 to balanced ternary form.

A: We will use basic knowledge of "order" and the number system, and ways to convert from one to…

Q: give the form for xp if the method of undetermined coefficients were to be used. You need not…

A: We have to give the form of particular solution using method of undetermined coefficient without…

Q: (x-1)2 (y+2)? What are the endpoints of the conjugate axis of 25 - 36 O (1 ± 5, –2) O (1, -2 ± 6) O…

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Q: Click and drag the steps to show that at least three of any 25 days chosen must fall in the same…

A: In discrete mathematics, there are two basic methods for proving a statement is true: proof by…

Q: Suppose that m andn are positive integers and b is a real number so that the principal n" root of b…

A: We have been given that nth root of b exists where b is the real number.

Q: 1. List the axioms of addition and multiplication for integers. 2. Using the axioms of the previous…

A: What is Integer: In mathematics, an integer is a grouping of positive and negative numbers. Like…

Q: . Let f (x) = 11x +9x +21. Prove that f (x) is irreducible over Q.

A: We solve this problem using  (mod p ) irreducibility test over f(x) where p = 2 , a prime number.

Q: 9. Show that 4x - 251 + 10x? – 15x + 20 is irreducible over Q.

A: Answer

Q: O Question 10 of 12 b=0b 0 (4 3i)(4+31) D 0 (4-3i)(1) (61)(4+31) (61) (1) D (-5)(4+3) D B (-5)(4)…

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Q: Q9. (a) (i) Calculate (2 + i√5)(√5 - i). (ii) Hence verify that (√5 - i) is a root of the equ

A: (a) The given expression is 2+i55-i Multiply the terms in the given expression…

Q: Prove by contradiction that there is no greatest multiple of 5.

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Q: 2.3.12 Prove Lemma 2.3.10 (2). Only need to prove #2 0f Lemma 2.3.10. Lemma 2.3.10. Let a E R. 1. a…

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Q: Q1. Solve the Following. i) (367)9 + (715)9 = ( ?)9 ii) (715)8 - (367)8 = ( ?)8 iii) (296)12 +…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Show that i e Q (/2 ). .

A: Show that i∉ℚ2.

Q: Find a composite transformation matrix composed of elementary rotations, Rx(0), Ry(0), and Rz(0)…

A: Sol